Travelling waves for the Gross-Pitaevskii equation II
arXiv:0711.2408 · doi:10.1007/s00220-008-0614-2
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.
Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remarks
References in corpus (3)
Cited by in corpus (5)
- Travelling waves for the Gross-Pitaevskii equation II
- Scattering theory for the Gross-Pitaevskii equation in three dimensions
- On the KP I transonic limit of two-dimensional Gross-Pitaevskii travelling waves
- Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation
- Global existence for defocusing cubic NLS and Gross-Pitaevskii equations in three dimensional exterior domains