Travelling waves for the Gross-Pitaevskii equation II
Fabrice Bethuel (LJLL), Philippe Gravejat (CEREMADE), Jean-Claude Saut, (LM-Orsay)
TL;DR
This paper rigorously proves the existence of traveling wave solutions to the Gross-Pitaevskii equation in 2D and 3D, extending previous results and showing the absence of small-energy solutions in 3D.
Contribution
It provides a complete branch of traveling wave solutions using minimization techniques, extending earlier partial results and establishing nonexistence of small-energy solutions in three dimensions.
Findings
Full branch of solutions established in 2D and 3D
No small-energy solutions in 3D
Extension of previous partial results
Abstract
The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield a full branch of solutions, and extend earlier results, where only a part of the branch was built. In dimension three, we also show that there are no travelling wave solutions of small energy.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.