Speaker
Description
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 will be given by a minimization procedure under constraint, but only when the width of the strip is large enough. Next a perturbative approach will provide a rigorous construction of two-dimensional stationary solutions with a fixed number of vortices, that are called solitonic vortices and were first described by numerical simulations and physical experiments in the context of the Bose-Einstein condensation.
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) and Étienne Sandier (Paris-East Créteil University) on the other hand.
