CERAMATHS - DMATHS seminar: presentation by André De Laire

The CERAMATHS Mathematics Department seminar will welcome André De Laire (Painlevé laboratory, University of Lille) at 2pm on Thursday, October 19, 2023, for the following talk:

 On traveling waves for some Gross-Pitaevskii equations

In this talk, we will discuss some properties of traveling waves solutions for some variants of the classical Gross-Pitaevskii equation in the whole space, in order to include new physical models in Bose-Einstein condensates and nonlinear optics. We are interested in the existence of finite energy localized traveling waves solutions with nonvanishing conditions at infinity, i.e. dark solitons. After a review of the state of the art in the classical case, we will show some results for a family of Gross-Pitaevskii equations with nonlocal interactions in the potential energy, obtained by variational techniques. Then, we will discuss the existence and behavior of the dark solitons for the Gross-Pitaevskii equation is a strip, according to its width.
This is joint work with Philippe Gravejat, Salvador Lopez-Martinez, and Didier Smets.