Travelling waves for the Gross-Pitaevskii equation in a strip

par Philippe Gravejat (Cergy)

jeudi 12 nov. 2026, 11:15 → 12:15 Europe/Paris

Salle J. Cavailles (1R2-132)

The talk deals with the Gross-Pitaevskii equation in a two-dimensional strip. This equation has explicit travelling wave solutions on the line that are called dark solitons and that remain travelling wave solutions on the strip. A natural question is to ask to what extent it is possible to construct true two-dimensional travelling waves in the strip.

A first answer is given by a minimization procedure under constraint, but only when the width of the strip is large enough. Next a perturbative approach provides two-dimensional travelling waves with small speeds, including stationary solutions with a fixed number of vortices, that are called solitonic vortices.

This is joint work with André de Laire (University of Lille) and Didier Smets (Sorbonne University) on the one hand, and with Amandine Aftalion (CNRS and University Paris Saclay), Shrish Parmeshwar (University of Bath) and Étienne Sandier (Paris-East Créteil University) on the other hand.