Numerical and analytical approaches for nonlinear dispersive PDEs

Liste des Contributions

24. P. Gérard

01/12/2025 09:45

A proof of the soliton resolution conjecture for the Benjamin-Ono equation
The soliton resolution conjecture for the Benjamin-Ono equation states that every solution on the line with a sufficiently smooth and decaying initial datum expands as time tends to infinity as a finite sum of decoupled soliton solutions added to a radiation term.
I will state a precise version of this conjecture...

25. J. He

01/12/2025 11:00

Explicit Formulas and the Zero-Dispersion Limit for the Benjamin–Ono Hierarchy on line

I will show how the Lax pair structure leads to the explicit formulas for the Benjamin–Ono Hierarchy on the line. Applications to the zero-dispersion limit for third order equation will be discussed. This work is in collaboration with Patrick Gérard.

26. S. Roudenko

01/12/2025 14:00

27. O. Maehlen

01/12/2025 15:15

The zero-dispersion limit for the Benjamin–Ono equation on the circle

Using the explicit formula of P. Gérard, we characterize the zero-dispersion limit for
solutions of the Benjamin–Ono equation on the circle with bounded initial dat. The result generalizes the work of L. Gassot, who focused on periodic bell-shaped data,
and complements the work of Gérard and X. Chen who identified...

28. T. Gaudry

01/12/2025 16:15

Numerical study of solutions to the Kaup-Broer-Kupershmidt systems

We will discuss recent numerical results on the Kaup–Broer–Kupershmidt (KBK) systems with a particular focus on line solitary waves and their transverse stability. We numerically construct a stationary solution and study its (in)stability. We introduce a dynamical rescaling to discuss a blow-up of the solutions.

29. L Gassot

02/12/2025 09:45

Global well-posedness for perturbations of the Benjamin-Ono equation on the torus

We prove global-wellposedness in the Sobolev spaces H^s for s>-1/2 for the Benjamin-Ono equation on the torus, perturbed by a class of zero-order Fourier multipliers. Examples of such equations include the periodic intermediate long wave equation. The method consists in using the Birkhoff map, that sends...

30. A. Ostermann

02/12/2025 11:00

A conservative dynamical low-rank algorithm

Kinetic equations present computational challenges due to their (up to) six-dimensional phase space dependence, resulting in high memory requirements and high computational cost. Traditional particle methods alleviate this burden, but generally suffer from noise. Dynamical low-rank approximation is a novel approach that significantly reduces...

31. P. Perry

02/12/2025 14:00

Large-Data Global Well-Posedness for the modified Novikov-Veselov (mNV) Equation

This is joint work with Adrian Nachman and Daniel Tataru. The  mNV equation is a nonlinear dispersive equation in two space dimensions, related to the Novikov-Veselov equation by a Miura-type map. Drawing on Nachman, Regev, and Tataru's work on global well-posedness for the Davey-Stewartson equation, we...

32. S. Gavrilyuk

02/12/2025 15:15

About the speed and amplitude of the leading edge of a dispersive shock wave

In 1850, at the age of 33, Ivan Aivazovsky, a Russian painter of Armenian origin, presented his major work, The Ninth Wave, to the Russian public. The painting depicts the sea after a cruel storm. The shipwrecked sailors, clinging to the mast of their destroyed ship, continue to fight for their lives. But the...

39. D. Sulz

02/12/2025 16:15

Time Integration in Quantum Dynamics using Tree Tensor Networks


This talk studies the numerical solution of high-dimensional tensor differential equations. The prohibitive computational cost and memory requirements of numerically simulating such equations are often referred to as the curse of dimensionality. Such prohibitively large differential equations arise in many fields of...

33. M. Akritidis

02/12/2025 17:15

Towards enhanced reconstruction quality in electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive imaging modality that reconstructs the spatial distribution of electrical conductivity or impedance within a body (e.g., lungs or brain) using boundary measurements from surface electrodes. Physically, EIT can be formulated as an inverse scattering problem,...

34. S. Abenda (online)

03/12/2025 09:45

Tropical curves and KP solitons: the case of banana graphs
The Kadomtsev–Petviashvili (KP) II equation is the first member of an integrable hierarchy in 2+1-variables, it contains as reductions other interesting integrable systems (Korteweg de Vries, Boussinesq, ...), and it possesses two distinguished classes of solutions:
1 KP-finite-gap solutions are parametrized by non special...

35. E. de Leon

03/12/2025 11:00

Numerical solutions of a class of evolution PDEs

In this talk I will present two different approaches to construct the numerical solution of a class of evolution PDEs, such as the Schrödinger equation. We consider a combination of parametrization (time-dependent complex parameters) and time discretization processes. The main differences regarding the order in which this combination is...

38. J.C. Saut

03/12/2025 14:00

On higher order nonlinear Schrödinger equations

We will survey results and open questions on various nonlinear Schrödinger equations occuring in water wave theory and nonlinear optics.

36. M. Fasondini

03/12/2025 15:15

A sparse spectral method on domains bounded by planar algebraic curves

We develop a sparse spectral method for solving partial differential equations on a class of two-dimensional geometries bounded by algebraic curves.  The numerical method uses generalised bivariate Koornwinder polynomials, which form a basis that is orthogonal but not ordered by degree.  The generalised Koornwinder...

37. M. Zejli

03/12/2025 16:15

Modeling binary black hole systems using a spacetime with helical symmetry

Binary black hole systems can be approximated as a single circular orbit at fixed separation, from large distances down to the innermost stable circular orbit (ISCO), where the gravitational energy lost through gravitational waves is exactly compensated by an incoming flux of gravitational waves from infinity. In...