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BEGIN:VEVENT
SUMMARY:A hybrid WKB-based method for Schrödinger scattering problems in
the semi-classical limit
DTSTART;VALUE=DATE-TIME:20190903T094500Z
DTEND;VALUE=DATE-TIME:20190903T103000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3964@indico.math.cnrs.fr
DESCRIPTION:Speakers: Anton Arnold (Vienna University of Technology)\n\nWe
consider 1D scattering problems related to quantum transport in diodes. W
e discuss the efficient numerical integration of ODEs like $\\epsilon^2*u"
+a(x)*u=0$ for $00$) and evanescent regimes (for $a(x)<0$)\, partly inclu
ding turning points. In the oscillatory case we use a marching method that
is based on an analytic WKB-preprocessing of the equation. And in the eva
nescent case we use a FEM with WKB-ansatz functions.\n\n(co-authors: Claud
ia Negulescu\; Kirian Döpfner\; Christian Klein\, Bernhard Ujvari)\n\nhtt
ps://indico.math.cnrs.fr/event/4493/contributions/3964/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3964/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The stability of periodic solutions of the focusing NLS equation
DTSTART;VALUE=DATE-TIME:20190903T123000Z
DTEND;VALUE=DATE-TIME:20190903T130000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3965@indico.math.cnrs.fr
DESCRIPTION:Speakers: Bernard Deconinck (University of Washington)\n\nA su
rprisingly large number of physically relevant dispersive partial differen
tial equations are integrable. Using the connection between the spectrum a
nd the eigenfunctions of the associated Lax pair and the linear stability
problem\, we investigate the stability of the spatially periodic traveling
wave solutions of such equations\, extending the results to orbital stabi
lity in those case where solutions are linearly stable. The talk will emph
asize recent results for the focusing NLS equation\, as this situation is
more complicated than that of other equations previously studied\, for whi
ch the Lax pair is self adjoint.\n\nhttps://indico.math.cnrs.fr/event/4493
/contributions/3965/
LOCATION:Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3965/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inverse Scattering for the Intermediate Long Wave Equation
DTSTART;VALUE=DATE-TIME:20190905T070000Z
DTEND;VALUE=DATE-TIME:20190905T074500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3977@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Perry (University of Kentucky)\n\nThis talk r
eports on joint work with Joel Klipfel (University of Kentucky) and Yilun
Wu (University of Oklahoma). The intermediate long wave equation (ILW) is
a model of weakly nonlinear wave propagation in a fluid of finite depth. I
t interpolates between the Benjamin-Ono equation (infinite depth) and the
Korteweg-de Vries equation (shallow water). Ablowitz and Kodama showed tha
t ILW is completely integrable and\, subsequently\, an inverse scattering
approach to solving ILW was developed by Ablowitz-Kodama-Satsuma and Santi
ni-Ablowitz-Fokas. Our work is\, to our knowledge\, the first rigorous ana
lysis of direct and inverse scattering maps for ILW. Both the direct and
inverse problems are Riemann-Hilbert problems (respectively local and non-
local)\; their proper formulation involves several interesting technical c
hallenges.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3977/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3977/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edge vectors on planar networks and tropical limit of real finite
gap solutions of KP hierarchy
DTSTART;VALUE=DATE-TIME:20190903T130000Z
DTEND;VALUE=DATE-TIME:20190903T133000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3966@indico.math.cnrs.fr
DESCRIPTION:Speakers: Simonetta Abenda (University of Bologna)\n\nIn this
talk\, I shall report on some recent results obtained in collaboration wit
h P.G. Grinevich (LITP\,RAS). We construct edge vectors on planar networks
obtained by gluing the positive part of copies of Gr(1\,3) and Gr(2\,3) a
nd apply such construction to associate real regular KP divisors on ration
al degenerations of M-curves.\n\nhttps://indico.math.cnrs.fr/event/4493/co
ntributions/3966/
LOCATION:Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3966/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a $\\partial\, \\overline{\\partial }$ system with a large para
meter.
DTSTART;VALUE=DATE-TIME:20190905T074500Z
DTEND;VALUE=DATE-TIME:20190905T083000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3978@indico.math.cnrs.fr
DESCRIPTION:Speakers: Johannes Sjöstrand (Université de Bourgogne)\n\nTh
is is part of a joint work with\nChristian Klein and Nikola Stoilov. We co
nsider a $2\\times 2$ system of $\\partial \,\\overline{\\partial }$ type
in the large parameter limit\, appearing in the study of the Davey-Stuarts
on II equation.\n\nWhen a certain potential is smooth\, we show that the s
olution is given by a convergent perturbation series.\n\nWhen it is the ch
aracteristic function of a strictly convex domain\, we analyze the leading
term in the series. Numerical simulations show a fairly good coincidence
with the full solution despite the lack of smoothness of the potential in
this case.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3978/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3978/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-ultralocality\, affine Gaudin models and Chern-Simons theory
DTSTART;VALUE=DATE-TIME:20190904T090000Z
DTEND;VALUE=DATE-TIME:20190904T093000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3968@indico.math.cnrs.fr
DESCRIPTION:Speakers: Benoit Vicedo (University of York)\n\nNon-ultralocal
ity is a long-standing open problem in classical integrable field theory w
hich has precluded the first-principle quantisation of many important mode
ls. I will review a recent proposal for dealing with this issue\, which re
lates it to the study of Gaudin models associated with affine Kac-Moody al
gebras. I will then go on to discuss its relation to another very recent p
roposal of Costello and Yamazaki who's starting point is a four-dimensiona
l variant of Chern-Simons theory.\n\nhttps://indico.math.cnrs.fr/event/449
3/contributions/3968/
LOCATION:C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3968/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Electrical Impedance Tomography and the Novikov-Veselov equation
DTSTART;VALUE=DATE-TIME:20190905T090000Z
DTEND;VALUE=DATE-TIME:20190905T094500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3979@indico.math.cnrs.fr
DESCRIPTION:Speakers: Samuli Siltanen (University of Helsinki)\n\nThe D-ba
r method\, introduced by Beals and Coifman in the 1980’s\, provides a so
lution method for Calderón’s inverse conductivity problem in dimension
two\, as was shown by Nachman in 1996. This presentation shows how Nachman
’s proof can be developed further to yield the D-bar method\, a practica
l imaging algorithm for Electrical Impedance Tomography (EIT). Furthermore
\, demonstrated is how machine learning can be combined with the D-bar met
hod for the diagnosis of stroke. Finally\, the nonlinear Novikov-Veselov e
quation can be solved using the inverse scattering method and the same non
linear Fourier transform than the one used in EIT.\n\nhttps://indico.math.
cnrs.fr/event/4493/contributions/3979/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3979/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrable coupled sigma-models from affine Gaudin models
DTSTART;VALUE=DATE-TIME:20190904T093000Z
DTEND;VALUE=DATE-TIME:20190904T100000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3969@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sylvain Lacroix (Universtät Hamburg)\n\nIn this tal
k\, we will discuss realisations of affine Gaudin models and their applica
tion to integrable sigma-models. After reviewing the properties of affine
Gaudin models and their relation with integrable sigma-models (see also B.
Vicedo's talk)\, we will explain a systematic procedure allowing to assem
ble two affine Gaudin models into a unique one. As an application of this
formalism\, we will present an integrable coupled sigma-model obtained by
assembling together N copies of the Principal Chiral Model with Wess-Zumin
o term.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3969/
LOCATION:C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3969/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a gas of soliton for the modified KdV equation
DTSTART;VALUE=DATE-TIME:20190904T073000Z
DTEND;VALUE=DATE-TIME:20190904T080000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3971@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tamara Grava (SISSA)\n\nWe study a gas of solitons i
n the limit when the number of solitons goes to infinity.\nWe characterize
the asymptotic behaviour and the long time behaviour of the soliton gas.\
n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3971/
LOCATION:C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3971/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Riemann-Hilbert approach to the lower tail of the KPZ equation
DTSTART;VALUE=DATE-TIME:20190904T080000Z
DTEND;VALUE=DATE-TIME:20190904T083000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3972@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mattia Cafasso (Université d'Angers)\n\nFredholm de
terminants associated to deformations of the Airy kernel are known to be c
losely connected to the solution to the Khardar-Parisi-Zhang (KPZ) equatio
n with narrow wedge initial data\, and they also appear as largest particl
e distribution in models of positive-temperature free fermions. It is of p
articular importance in these models to understand the lower tail of the F
redholm determinants.\nWe show that logarithmic derivatives of the Fredhol
m determinants can be expressed in terms of a 2×2 Riemann-Hilbert problem
\, and we use this to derive asymptotics for the Fredholm determinants. As
an application of our result\, we derive precise lower tail asymptotics f
or the solution of the KPZ equation with narrow wedge initial date\, thus
refining recent results by Corwin and Ghosal.\n\nhttps://indico.math.cnrs.
fr/event/4493/contributions/3972/
LOCATION:C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3972/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrable and near-integrable long-wave models in stratified shea
r flows
DTSTART;VALUE=DATE-TIME:20190902T150000Z
DTEND;VALUE=DATE-TIME:20190902T153000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3959@indico.math.cnrs.fr
DESCRIPTION:Speakers: Karima Khusnutdinova (Loughborough University)\n\nIn
this talk I will overview recent developments concerning a version of the
Kadomtsev-Petviashvili (KP) equation for surface gravity waves related to
elliptic-cylindrical geometry\, a system of coupled Ostrovsky equations d
erived for strongly interacting internal waves in the presence of backgrou
nd rotation and a shear flow\, and 2+1-dimensional cylindrical Korteweg-de
Vries (cKdV)-type model describing ring waves in a stratified fluid in th
e presence of a depth-dependent parallel shear flow.\n\nhttps://indico.mat
h.cnrs.fr/event/4493/contributions/3959/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3959/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stratified 2D Euler Flows: Hamiltonian aspects\, conserved quantit
ies and classes of solutions.
DTSTART;VALUE=DATE-TIME:20190904T070000Z
DTEND;VALUE=DATE-TIME:20190904T073000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3974@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gregorio Falqui (University of Milano-Bicocca)\n\nht
tps://indico.math.cnrs.fr/event/4493/contributions/3974/
LOCATION:C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3974/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bloch spectrum for water waves
DTSTART;VALUE=DATE-TIME:20190902T070000Z
DTEND;VALUE=DATE-TIME:20190902T074500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3951@indico.math.cnrs.fr
DESCRIPTION:Speakers: Catherine Sulem (University of Toronto)\n\nWe examin
e the motion of the free surface of a body of fluid with a periodically va
rying bottom. We consider the water wave system linearized near a stationa
ry state and develop a Bloch theory. The analysis takes the form of a spec
tral problem for the Dirichlet– Neumann operator in a fluid domain with
a periodic bottom and a flat surface elevation. We find that\, generically
\, the presence of the bottom results in the splitting of double eigenvalu
es creating a spectral gap. The analysis is uniform in the spectral parame
ter and provides the gap asymptotics.\n\nhttps://indico.math.cnrs.fr/event
/4493/contributions/3951/
LOCATION:Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3951/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrability of new class of hyperbolic two-dimensional linear eq
uations of second order
DTSTART;VALUE=DATE-TIME:20190902T153000Z
DTEND;VALUE=DATE-TIME:20190902T160000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3960@indico.math.cnrs.fr
DESCRIPTION:Speakers: Maxim Pavlov (Lebedev Physical Institute of Russian
Academy of Sciences)\n\nWe consider a linear two-dimensional hyperbolic eq
uation of second order\, whose coefficients are polynomials with respect t
o one of independent variables.\n \nWe show that this equation possesses i
nfinitely many particular solutions\, determined by solutions of ordinary
differential equations.\n\nhttps://indico.math.cnrs.fr/event/4493/contribu
tions/3960/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3960/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrable Lagrangians and Picard modular forms
DTSTART;VALUE=DATE-TIME:20190905T131500Z
DTEND;VALUE=DATE-TIME:20190905T140000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3993@indico.math.cnrs.fr
DESCRIPTION:Speakers: Evgeny Ferapontov (Loughborough University)\n\nWe co
nsider first-order Lagrangians whose Euler-Lagrange equations belong to th
e class of 3D dispersionless integrable systems. Our main results can be s
ummarised as follows:\n(1) A link between integrable Lagrangians and Picar
d curves/Picard modular forms studied by E. Picard as far back as in 1883
is established.\n(2) A parametrisation of integrable Lagrangian densities
by generalised hypergeometric functions (solutions of the Picard-Fuchs sys
tem governing periods of Picard curves) is obtained.\n(3) Conjectured thet
a representations and power series expansions of the integrable Lagrangian
densities are proved.\n(based on joint work with F. Cl\\'ery A. Odesskii
and D. Zagier)\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/399
3/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3993/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Novikov algebras and Darboux coordinate: the construction of flat
coordinates
DTSTART;VALUE=DATE-TIME:20190905T123000Z
DTEND;VALUE=DATE-TIME:20190905T131500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3992@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ian Strachan (University of Glasgow)\n\nThe classica
l Muira maps transforms the second Hamiltonian structure of the KdV hierar
chy into constant\, or Darboux\, form. In this talk multi-component versio
ns of this map are constructed\, for Hamiltonian structures defined by Nov
ikov algebras.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/399
2/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3992/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sine-Gordon field theory vs. relativistic Calogero-Moser $N$-parti
cle sytems
DTSTART;VALUE=DATE-TIME:20190905T094500Z
DTEND;VALUE=DATE-TIME:20190905T103000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3989@indico.math.cnrs.fr
DESCRIPTION:Speakers: Simon Ruijsenaars (University of Leeds)\n\nWe survey
the relation between the relativistic sine-Gordon model and (a special ca
se of) the hyperbolic relativistic integrable $N$-particle systems of Calo
gero-Moser type. More specifically\, we review the intimate link between t
he classical version of the latter and the particle-like sine-Gordon solut
ions\, and present compelling evidence that this soliton-particle correspo
ndence turns into a physical equivalence on the quantum level\, in the se
nse that the same scattering amplitudes and bound state energies arise i
n the quantum field-theoretic and $N$-particle models.\n\nhttps://indico.m
ath.cnrs.fr/event/4493/contributions/3989/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3989/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On some (non-integrable) KP type equations
DTSTART;VALUE=DATE-TIME:20190906T094500Z
DTEND;VALUE=DATE-TIME:20190906T103000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3987@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean-Claude Saut (Universite Paris-Sud)\n\nWe presen
t recent results and open issues on KP-type equations arising in the model
ing of internal waves\n\nhttps://indico.math.cnrs.fr/event/4493/contributi
ons/3987/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3987/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Universality in Random Tiling Models
DTSTART;VALUE=DATE-TIME:20190906T070000Z
DTEND;VALUE=DATE-TIME:20190906T074500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3990@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pierre van Moerbeke (University of Louvain and Brand
eis University)\n\nTilings of polygonal regions with non-convexities (cuts
) lead to a new kernel and a new statistics for the asymptotic fluctuation
s of the tiles\, when the size of the region and the cuts gets large under
an appropriate scaling. The limiting statistics has been observed in very
different circumstances.\n\nhttps://indico.math.cnrs.fr/event/4493/contri
butions/3990/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3990/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiple rogue waves and integrable models: perspectives and retro
spectives
DTSTART;VALUE=DATE-TIME:20190906T074500Z
DTEND;VALUE=DATE-TIME:20190906T083000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3991@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vladimir Matveev (Université de Bourgogne)\, Alexan
der Smirnov (St.-Petersburg State University )\n\nThis talk is dedicated
to the description of the modulation instabilities\, leading to the appea
rance of phenomena of multiple rogue waves generation in a frame of integr
able hierarchies. It is mainly concentrated on the AKNS hierarchy and some
related systems.\nAn essential part of the results is exposed in our rece
nt article: V.B. Matveev\, A.O. Smirnov "AKNS and NLS hierarchies\, MRW s
olutions\, P_n breathers\, and beyond"\, J.Math. Phys. 59\, 091419(2018)\;
doi: 10.1063/1.5049949\n\nhttps://indico.math.cnrs.fr/event/4493/contribu
tions/3991/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3991/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tropical limit of matrix solitons
DTSTART;VALUE=DATE-TIME:20190903T150000Z
DTEND;VALUE=DATE-TIME:20190903T153000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3984@indico.math.cnrs.fr
DESCRIPTION:Speakers: Folkert Müller-Hoissen (University of Goettingen)\n
\nThe "tropical limit'' of a matrix (KdV\, Boussinesq\, or the like) solit
on solution in two-dimensional space-time consists of a piecewise linear g
raph in space-time\, together with values of the dependent variable along
its segments. In two space-time dimensions\, it associates with such wave
s a point particle picture\, in which free "particles'' with internal degr
ees of freedom interact at definite points in space-time. Whereas for KdV
the values of the dependent variable attached to incoming and outgoing sol
itons at a vertex are related by a (highly nonlinear) Yang-Baxter map\, su
ch a map appears to be insufficient in the Boussinesq case to describe all
possible soliton interactions in the tropical limit. The interaction in c
ase of solitons in more than two dimensions is definitely richer. We will
report about some insights for soliton solutions of the KP equation. \nTh
is talk is based on joint work with A. Dimakis [1\,2\,3] and X.-M. Chen [3
].\n[1] A. Dimakis and F. Müller-Hoissen: Matrix KP: tropical limit and Y
ang-Baxter maps\, Lett. Math. Phys. 109 (2019) 799-827.\n[2] A. Dimakis an
d F. Müller-Hoissen: Matrix KP: tropical limit\, Yang-Baxter and pentagon
maps\, Theor. Math. Phys. 196 (2018) 1164-1173.\n[3] A. Dimakis\, F. Mül
ler-Hoissen and X.-M. Chen: Matrix Boussinesq solitons and their tropical
limit\, Physica Scripta 94 (2019) 035206.\n\nhttps://indico.math.cnrs.fr/e
vent/4493/contributions/3984/
LOCATION:Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3984/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Strongly interacting soliton gas and the noise-induced modulation
instability
DTSTART;VALUE=DATE-TIME:20190905T150000Z
DTEND;VALUE=DATE-TIME:20190905T153000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-4019@indico.math.cnrs.fr
DESCRIPTION:Speakers: Andrey Gelash (Skolkovo Institute of Science and Tec
hnology)\n\nWe investigate the statistically stationary state of spontaneo
us noise-driven modulation instability of a plane wave (condensate) backgr
ound. As a model we use the integrable focusing one-dimensional nonlinear
Schrodinger equation (NLSE). The fundamental statistical characteristics o
f the stationary state of the modulation instability obtained numerically
by Agafontsev and Zakharov in 2015 [1] have not been explained so far. Whe
n the condensate is spatially wide the inverse scattering transform (IST)
theory predicts that interacting solitons play the dominating role in the
system evolution. Here we explain statistical characteristics of the modul
ation instability by using N-soliton solutions (N-SS\, here N means the nu
mber of solitons) of the NLSE. We determine parameters of the N-SS corresp
onding to the statistically stationary state of the integrable turbulence
produced by the instability development. These N-SS are strongly interacti
ng bound states of solitons having specific distribution of the IST eigenv
alues and random phases. The condensate is a coherent state of the N-SS an
d initial stage of the modulation instability development represents the l
oss of coherence of the soliton phases. We use a special approach to const
ruct ensembles of the multi-soliton solutions with statistically large num
ber of solitons N ~100 [2]. Our investigation demonstrates complete agreem
ent in spectral and statistical properties of the long-term evolution of t
he condensate perturbed by noise and the constructed multisoliton bound st
ates [3]. Our results can be generalised to the broad class of integrable
turbulence problems in the cases when the wave filed dynamics is strongly
nonlinear and driven by solitons.\n\n[1] D. Agafontsev and V. E. Zakharov\
, Nonlinearity 28\, 2791 (2015)\n[2] A. A. Gelash and D. S. Agafontsev\, P
hys. Rev. E 98\, 042210 (2018).\n[3] A. Gelash\, D. Agafontsev\, V. Zakhar
ov\, G. El\, S. Randoux and P. Suret\, Bound state soliton gas dynamics un
derlying the noise-induced modulational instability\, In preparation.\n\nh
ttps://indico.math.cnrs.fr/event/4493/contributions/4019/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/4019/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A complex-analysis friendly form of Schroedinger equation with a n
on-vanishing potential
DTSTART;VALUE=DATE-TIME:20190905T153000Z
DTEND;VALUE=DATE-TIME:20190905T160000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-4020@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmitry Ponomarev (TU Wien)\n\nThe aim of the talk is
to introduce a transformation which reduces initial-value problem for one
-dimensional Schroedinger equation with a non-vanishing potential to an el
ementary homogeneous first-order nonlinear ODE. The latter exhibits nonlin
earity merely as complex conjugation and hence is very amenable to applica
tion of transform methods and further complex-analytic treatment. The obta
ined reformulation is beneficial for both analytical and practical purpose
s such as simplification of construction of efficient hybrid asymptotical-
numerical schemes for oscillatory quasi-classical regime\, a new form of P
rufer equations and new classes of solvable potentials due to reduction to
an integral equation of convolution type on a half-line.\n\nhttps://indic
o.math.cnrs.fr/event/4493/contributions/4020/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/4020/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The quantum beating and its numerical simulation
DTSTART;VALUE=DATE-TIME:20190903T090000Z
DTEND;VALUE=DATE-TIME:20190903T094500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3963@indico.math.cnrs.fr
DESCRIPTION:Speakers: Claudia Negulescu (Univ. Paul Sabatier)\n\nQuantum b
eating may nowadays refer to many\, often quite different phenomena studie
d in various domains of quantum physics. A paradigmatic example is the inv
ersion in the ammonia molecule\, observed experimentally in 1935. \nA theo
retical explanation of the quantum beating was obtained by modelling the n
itrogen atom as a quantum particle in a double well potential. The quantum
environment of this particle can be modelled as a non-linear perturbation
term added to the double well potential.\n\nIn this talk\, I shall examin
e numerically the suppression of the quantum beating in a one dimensional
non-linear double well potential\, made up of two focusing nonlinear point
interactions. The study of the Schroedinger dynamics is reduced to the st
udy of a system of coupled nonlinear Volterra integral equations. I will s
how that already for a nonlinearity exponent well below the critical value
\, there is complete suppression of the typical beating behaviour characte
rizing the linear quantum case.\n\nhttps://indico.math.cnrs.fr/event/4493/
contributions/3963/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3963/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monodromy dependence of Painlevé tau functions
DTSTART;VALUE=DATE-TIME:20190902T123000Z
DTEND;VALUE=DATE-TIME:20190902T130000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3955@indico.math.cnrs.fr
DESCRIPTION:Speakers: Oleg Lisovyi (Université de Tours)\n\nIn many inter
esting cases\, distribution functions of random matrix theory and correlat
ion functions of integrable models of statistical mechanics and quantum C-
field theory are given by tau functions of Painlevé equations. I will dis
cuss an extension of the Jimbo-Miwa-Ueno differential to the space of mono
dromy data and explain how this construction can be used to compute consta
nt terms in the tau function asymptotics.\n\nhttps://indico.math.cnrs.fr/e
vent/4493/contributions/3955/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3955/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The direct problem of perturbed KPII multi-line solitons
DTSTART;VALUE=DATE-TIME:20190904T100000Z
DTEND;VALUE=DATE-TIME:20190904T103000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3982@indico.math.cnrs.fr
DESCRIPTION:Speakers: Derchyi Wu (Academica Sinica\, Taipei)\n\nBoiti-Pemp
inelli-Pogrebkov's inverse scattering theories on the KPII equation provid
e an integrable approach to solve the Cauchy problem of the perturbed KPII
multi-line soliton solutions and the stability problem of KPII multi-line
solitons.\n\nIn this talk\, we will present rigorous analysis for the dir
ect scattering theory of perturbed KPII multi line solitons\, illustrat
ed by perturbations of low dimensional Grassmannian cases.\n\nhttps://indi
co.math.cnrs.fr/event/4493/contributions/3982/
LOCATION:C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3982/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On dressing factors of 2-dimensional Toda field theories and mul
ticomponent MKdV equations
DTSTART;VALUE=DATE-TIME:20190903T153000Z
DTEND;VALUE=DATE-TIME:20190903T160000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-4018@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vladimir Gerdjikov (Bulgarian Academy of Sciences)\n
\nhttps://indico.math.cnrs.fr/event/4493/contributions/4018/
LOCATION:Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/4018/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Extended Lagrangian approach for the defocusing Non-Linear Schröd
inger equation
DTSTART;VALUE=DATE-TIME:20190902T143000Z
DTEND;VALUE=DATE-TIME:20190902T150000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3958@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sergey Gavrilyuk (Aix-Marseille Université)\n\nWe s
tudy the defocusing Non-Linear Schrödinger (NLS) equation written in hydr
odynamic form through the Madelung transform. From the mathematical point
of view\, the hydrodynamic form can be seen as the Euler-Lagrange equatio
ns for a Lagrangian submitted to a differential constraint corresponding t
o the mass conservation law. The dispersive nature of the NLS equation pos
es some major numerical challenges. The idea is to introduce a two-paramet
er family of extended Lagrangians\, depending on a greater number of varia
bles\, whose Euler-Lagrange equations are hyperbolic and accurately approx
imate NLS equation in a certain limit. The corresponding hyperbolic equat
ions are studied and solved numerically using Godunov type methods. Compa
rison of exact and asymptotic solutions to the one-dimensional cubic NLS e
quation (`grey' solitons and dispersive shocks) and the corresponding num
erical solutions to the extended system was performed. A very good accura
cy of such a hyperbolic approximation was observed. This is a joint talk w
ith Firas Dhaouadi and Nicolas Favrie.\n\nhttps://indico.math.cnrs.fr/even
t/4493/contributions/3958/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3958/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the derivative nonlinear Schrödinger equation related to symme
tric spaces
DTSTART;VALUE=DATE-TIME:20190903T133000Z
DTEND;VALUE=DATE-TIME:20190903T140000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3967@indico.math.cnrs.fr
DESCRIPTION:Speakers: Georgi Grahovski (University of Essex)\n\nWe will pr
esent multi-component generalizations of derivative nonlinear Schrödinger
(DNLS) type of equations having quadratic bundle Lax pairs related to $\\
mathbb{Z}_2$-graded Lie algebras and A.III symmetric spaces. The Jost sol
utions and the minimal set of scattering data for the case of local and no
nlocal reductions are constructed.\n\nFurthermore\, the fundamental analyt
ic solutions (FAS) are constructed and the spectral properties of the asso
ciated Lax operators are briefly discussed. The Riemann-Hilbert problem (R
HP) for the multi-component generalizations of DNLS equation of Kaup-Newel
l (KN) and Gerdjikov-Ivanov (GI) types is derived. A modification of the d
ressing method is presented allowing the explicit derivation of the solit
on solutions for the multi-component GI equation with both local and nonlo
cal reductions. \n\nThe infinite set of integrals of motion for these mode
ls is briefly described at the end.\n\nBased on a joint work with Vladimir
Gerdjikov and Rossen Ivanov.\n\n[1] Gerdjikov V.S\, Grahovski G.G. and Iv
anov R.I.\, On integrable wave interactions and Lax pairs on symmetric spa
ces\, Wave Motion 71 (2017)\, 53--70\, E-print: arXiv:1607.06940.\n\nhttps
://indico.math.cnrs.fr/event/4493/contributions/3967/
LOCATION:Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3967/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The non-commutative KdV equation and enumerative geometry
DTSTART;VALUE=DATE-TIME:20190902T133000Z
DTEND;VALUE=DATE-TIME:20190902T140000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3957@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paolo Rossi (Università degli Studi di Padova)\n\nI
n the past years\, in a joint project with A. Buryak\, we have developed a
general framework to construct classical and quantum field systems (in on
e space and one time dimensions) from intersection theory of the moduli sp
ace of stable curves. Recently a particularly interesting example came und
er our attention\, which actually produces a integrable system of Hamilton
ian PDEs in two space and one time dimensions. Computations of quadratic d
ouble ramification integrals\, an entirely natural problem in algebraic ge
ometry\, turn out to produce a interesting generalization of the KdV hiera
rchy to 2 non-commutative space dimensions (KdV on a noncommutative Moyal
torus).\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3957/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3957/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Birkhoff coordinates for the Benjamin-Ono equation on the torus
and applications to solutions with negative Sobolev regularity. Part 1
DTSTART;VALUE=DATE-TIME:20190902T074500Z
DTEND;VALUE=DATE-TIME:20190902T083000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3952@indico.math.cnrs.fr
DESCRIPTION:Speakers: Patrick Gérard (Université Paris-Sud)\n\nThis talk
is a survey of a recent joint work with Thomas Kappeler about the constru
ction of Birkhoff coordinates for real valued\, spatially periodic and squ
are integrable solutions of the Benjamin-Ono equation.\n\nhttps://indico.m
ath.cnrs.fr/event/4493/contributions/3952/
LOCATION:Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3952/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Birkhoff coordinates of the Benjamin-Ono equation on the torus
and applications to solutions with negative Sobolev regularity. Part 2
DTSTART;VALUE=DATE-TIME:20190902T090000Z
DTEND;VALUE=DATE-TIME:20190902T094500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3953@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thomas Kappeler (University of Zurich)\n\nIn this ta
lk I report on joint work with Patrick Gérard and Peter Topalov concernin
g properties of the flow map of the Benjamin-Ono equation on the torus. Th
e main result says that the flow map\, introduced in our previous work on
the space $L^2_{r\,0}$ of real valued\, $2\\pi-$periodic $L^2-$functions w
ith mean $0$\, \ncan be extended to the Sobolev spaces $H^{-s}_{r\,0}$ for
$0 < s < 1/2$. The key ingredient is a corresponding extension of the Bir
khoff coordinates to these Sobolev spaces.\n\nhttps://indico.math.cnrs.fr/
event/4493/contributions/3953/
LOCATION:Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3953/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Short review of results on Isomonodromy Deformations and Applicati
ons
DTSTART;VALUE=DATE-TIME:20190902T130000Z
DTEND;VALUE=DATE-TIME:20190902T133000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3956@indico.math.cnrs.fr
DESCRIPTION:Speakers: Davide Guzzetti (SISSA)\n\nSome results on non-gener
ic isomonodormy deformations\, already presented in other conferences and
seminars is some detail\, will be here reviewed in 25 minutes\, stressing
their relevance for computations involving Painleve' equations and Dubrov
in-Frobenius Manifolds. From joint works with G. Cotti and B. Dubrovin\n\n
https://indico.math.cnrs.fr/event/4493/contributions/3956/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3956/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conformal Fishnet Theory
DTSTART;VALUE=DATE-TIME:20190903T070000Z
DTEND;VALUE=DATE-TIME:20190903T074500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3961@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vladimir Kazakov (Ecole Normale Superieure\, Univ. S
orbonne)\n\nI will review the propreties and recent results for conformal
fishnet theory (FCFT) which was proposed by O.Gurdogan and myself as a sp
ecial double scaling limit of gamma-twisted N=4 SYM theory. FCFT\, in its
simplest\, bi-scalar version\, is a UV finite strongly coupled 4-dimensio
nl logarithmic CFT dominated by planar fishnet Feynman graphs (of the sha
pe of regular square lattice). FCFT inherits the planar integrability of
N=4 SYM which becomes manifest in this case: the fishnet graphs can be
mapped on the SO(2\,4) integrable spin chain (A.Zamolodchikov 1980). The
D-dimensional generalization of FCFT\, with SO(2\,D) conformal symmetry c
an be also provided. A remarkable property of FCFT is the possibility of
spontaneous symmetry breaking\, which is not lifted by quantum corrections
. I will also discuss the exact computation of certain anomalous dimension
s and 4-point correlators\, and of related fishnet Feynman graphs (of "w
heel" or "spiral" type)\, using the quantum integrability tools: asymptoti
c and thermodynamic Bethe ansatz and quantum spectral curve.\n\nhttps://in
dico.math.cnrs.fr/event/4493/contributions/3961/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3961/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Field-theoretical formulation of the Thermodynamic Bethe Ansatz
DTSTART;VALUE=DATE-TIME:20190903T074500Z
DTEND;VALUE=DATE-TIME:20190903T083000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3962@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ivan Kostov (IPhT Saclay)\n\nWe construct a quantum
system which generates the finite size effects in massive integrable model
s of QFT. The quantum system is built on a pair of operators creating part
icles wrapping the space and the time directions. The two wrapping operato
rs are given a representation as vertex operators for a pair of free boson
ic fields. The partition function at finite volume is represented as the e
xpectation value of an operator creating the ensemble of virtual particles
wrapping the space direction. This operator simplifies after approximatin
g the sum over mode numbers by an integral over the rapidities. The non-tr
ivial measure in the rapidity space requires adding a pair of fermionic pa
rtners of the two bosonic fields. The expectation value is formulated as a
path integral which localises to the critical point described by the TBA
equations. We restrict ourselves to a field theory with a single particle
with factorised scattering and no bound states\, such as the sinh-Gordon m
odel. Both periodic and open boundary conditions are considered. In case o
f periodic boundary conditions the loop effects due to bosons and fermions
compensate completely while for open boundary conditions the one-loop con
tribution gives the universal part of the boundary free energy.\n\nhttps:/
/indico.math.cnrs.fr/event/4493/contributions/3962/
LOCATION:Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3962/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asymptotic stability in 3d Zakharov-Kuznetsov equation
DTSTART;VALUE=DATE-TIME:20190906T090000Z
DTEND;VALUE=DATE-TIME:20190906T094500Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3988@indico.math.cnrs.fr
DESCRIPTION:Speakers: Svetlana Roudenko (Florida International University)
\n\nWe consider Zakharov-Kuznetsov (ZK) equation\, a higher-dimensional ge
neralization of the well-known KdV equation. We discuss the behavior of so
lutions close to the solitary wave given by Q(x-t\,y\,z) with Q being the
standard ground state.\nWe discuss the stability of solitary waves in the
3d quadratic (subcritical) ZK equation\, proving that solutions in the ene
rgy space that are orbitally stable (which is due to de Bouard) are also a
symptotically stable\, that is\, as time goes to infinity\, they converge
to a rescaling and shift of Q(x-t\,y\,z) in some rightward moving window.
While the local and global well-posedness is currently available only in h
igher regularity spaces (than finite energy) and due to Ribaud-Vento and M
olinet-Pilod\, we nevertheless obtain asymptotic stability in the energy s
pace. This is a joint work with Luiz Gustavo Farah\, Justin Holmer\, and K
ai Yang.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3988/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3988/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Numerical study of the Davey-Stweartson equation
DTSTART;VALUE=DATE-TIME:20190903T143000Z
DTEND;VALUE=DATE-TIME:20190903T150000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3976@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nikola Stoilov (Université de Bourgogne)\n\nIn this
work we will look at the focusing Davey-Stewartson equation from two diff
erent angles\, using advanced numerical tools.\nAs a nonlinear dispersive
PDE and a generalisation of the non-linear Schrödinger equation\, DS poss
esses solutions that develop a singularity in finite time. We numerically
study the long time behaviour and potential blow-up of solutions to the fo
cusing Davey-Stewartson II equation for various initial data and propose a
conjecture describing the blow up rate and solution profiles near the sin
gularity.\nSecondly\, DS is an integrable system and can be studied as an
inverse scat- tering problem. Both the forward and inverse scattering tran
sformation in this case are reduced to a d-bar system which plays the role
that Riemann-Hilbert problems play in one dimensional problems. We will p
resent numerical solutions for Schwartzian and compactly supported potenti
als. In all studied cases we use spectral methods and achieve machine prec
ision.\n\nBased on joint works with Christian Klein and Ken McLaughlin\n\n
https://indico.math.cnrs.fr/event/4493/contributions/3976/
LOCATION:Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3976/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hydrodynamics for integrable systems
DTSTART;VALUE=DATE-TIME:20190902T094500Z
DTEND;VALUE=DATE-TIME:20190902T103000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3954@indico.math.cnrs.fr
DESCRIPTION:Speakers: Benjamin Doyon (King's college London)\n\nHydrodynam
ics is a powerful framework for large-wavelength phenomena in many-body sy
stems. It was extended recently to include integrable models\, giving ``ge
neralised hydrodynamics”. In this talk\, I will review fundamental aspec
ts of the hydrodynamic of integrable systems\, with the simple examples of
the quantum Lieb-Liniger and the classical Toda models. I will then show
some of the exact results that can be obtained with this formalism\, such
as exact nonequilibrium steady states and exact asymptotic of correlation
functions at large space-time separations in Gibbs and generalised Gibbs s
tates\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3954/
LOCATION:Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3954/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rational spin chains at higher rank: new tools to solve\, complete
ness\, and separation of variables
DTSTART;VALUE=DATE-TIME:20190905T143000Z
DTEND;VALUE=DATE-TIME:20190905T150000Z
DTSTAMP;VALUE=DATE-TIME:20221001T164800Z
UID:indico-contribution-3970@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmytro Volin (Uppsala University and Nordita)\n\nWe
present recent advances in solution of rational spin chains that build on
results from representation theory of Yangian and analytic Bethe Ansatz. F
irst we show how to find spectrum of supersymmetric GL(N|M) chains using Q
-system on Young diagrams. This approach can be more efficient than conven
tional nested Bethe equations\, and also it provides one with means for ex
plicitly counting solutions and hence for proving completeness. Second\, w
e discuss the separation of variables program for GL(N) chains with generi
c twist and inhomogeneities and\, notably\, in arbitrary finite-dimensiona
l representation. For them\, we present an SoV basis in which eigenstates
are products of Slater determinants of Baxter Q-functions and discuss its
connection to Gelfand-Tsetlin patterns and to generalisations of Sklyanin
B-operator.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3970/
LOCATION:Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3970/
END:VEVENT
END:VCALENDAR