A uniqueness result for travelling waves in the Gross-Pitaevskii equation

Abstract

This note is a summary of a series of papers [12], [13] and [14], done in collaboration with David Chiron. In them, we establish the uniqueness of the energy minimizer at fixed large momentum for the 2 dimensional Gross-Pitaevskii equation, up to the natural invariances of the problem. The minimizer is a nonradial travelling wave with a small speed, behaving like two well separated vortices. Here, we summarize the key steps of the proof, highlighting the arguments that can be used for similar problems in other equations.