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

Eliot Pacherie

doi:10.5802/slsedp.148

Eliot Pacherie ¹

¹ NYUAD Research Institute, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE

Séminaire Laurent Schwartz — EDP et applications (2021-2022), Talk no. 17, 16 p.

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.

Published online: 2022-06-22

DOI: 10.5802/slsedp.148

Author's affiliations:

Eliot Pacherie ¹

¹ NYUAD Research Institute, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE

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Eliot Pacherie. A uniqueness result for travelling waves in the Gross-Pitaevskii equation. Séminaire Laurent Schwartz — EDP et applications (2021-2022), Talk no. 17, 16 p. doi : 10.5802/slsedp.148. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.148/

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