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SUMMARY:Grassmann-extended nonlinear Schrödinger equations: discretisatio
ns and Yang-Baxter maps
DTSTART;VALUE=DATE-TIME:20181129T153000Z
DTEND;VALUE=DATE-TIME:20181129T163000Z
DTSTAMP;VALUE=DATE-TIME:20190923T044733Z
UID:indico-event-4177@indico.math.cnrs.fr
DESCRIPTION:Georgi G. Grahovski - University of Essex\n\nRésumé : A rev
iew of integrable discretisations for a class of coupled nonlinear Schr¨o
dinger (NLS) type of equations are presented. The class corresponds to a L
ax operator with entries in a Grassmann algebra. Elementary Darboux transf
ormations are presented. As a result\, Grassmann generalisations of the To
da lattice and the NLS dressing chain are obtained. The compatibility (Bia
nchi commutativity) of these Darboux transformations leads to integrable G
rassmann generalisations of the difference Toda and NLS equations. The res
ulting discrete systems will have Lax pairs provided by the set of two con
sistent Darboux transformations. Finally\, Yang-Baxter maps for the Grassm
ann-extended NLS equation will be presentes. In particular\, we present te
n-dimensional maps which can be restricted to eight-dimensional Yang-Baxte
r maps on invariant leaves\, related to the Grassmann-extended NLS and DNL
S equations. Their Liouville integrability will be briefly discussed. Base
d on a joint work with A. V. Mikhailov and S. G. Konstantinou-Rizos.\n\nht
tps://indico.math.cnrs.fr/event/4177/
LOCATION:IMB René Baire
URL:https://indico.math.cnrs.fr/event/4177/
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