Guest Lecture: Charles Collot

Dynamics around self-similar solutions in evolution PDEs, with the example of a soliton in 1d nonlinear Schrodinger equations

Charles Collot is Chaire Professor Junior at CY Cergy Paris Université, in the AGM laboratory

In the area of nonlinear evolution partial differential equations, one research direction has become a major one over the last 30 years: studying the role played by self-similar solutions in the dynamics. Self-similar solutions are those that keep the same shape over time up to renormalisation, like stationary states, traveling waves, etc... The first part of the talk will introduce the soliton resolution conjecture, which states that for many PDEs, in certain contexts, general solutions are expected to decompose asymptotically in time into a sum of such self-similar solutions plus a lower order radiation. I will then illustrate this asymptotic description with some results I obtained, including examples of solutions for which these self-similar solutions produce remarkable concentration and propagation effects. The last part will focus on the example of 1D nonlinear Schrodinger equations. I will present a recent work with P. Germain (Imperial College, London) in which we establish the asymptotic stability of traveling waves through long-range scattering for the radiation.


Date: 19 December 2023 from 14:00 to 15:30

The hybrid guest lecture is organised in person at the H008 Meeting Room of MIR in Neuville-sur-Oise and remotely on Zoom.

To attend the remote guest lecture, please connect to Zoom: https://cyu-fr.zoom.us/j/93689087766

Meeting ID: 936 8908 7766

The video will be online on the CY AS YouTube channel

Photo credits: Archives of the Mathematisches Forschungsinstitut Oberwolfach