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Travelling Waves for the Gross-Pitaevskii Equation II

- F. Béthuel, Philippe Gravejat, J. Saut
- Mathematics
- 15 November 2007

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… Expand

Orbital stability of the black soliton to the Gross-Pitaevskii equation

- Fabrice B'ethuel, Philippe Gravejat, J. Saut, D. Smets
- Physics, Mathematics
- 4 April 2008

We establish the orbital stability of the black soliton, or kink solution, $\v_0(x) = \th \big( \frac{x}{\sqrt{2}} \big)$, to the one-dimensional Gross-Pitaevskii equation, with respect to… Expand

Asymptotic stability of the black soliton for the Gross–Pitaevskii equation

- Philippe Gravejat, D. Smets
- Physics
- 1 August 2015

We introduce a new framework for the analysis of the stability of solitons for the one-dimensional Gross-Pitaevskii equation. In particular, we establish the asymptotic stability of the black soliton… Expand

Asymptotics for the travelling waves in the Gross-Pitaevskii equation

- Philippe Gravejat
- Mathematics
- 2005

We investigate the asymptotic behaviour of the subsonic travelling waves of finite energy in the Gross-Pitaevskii equation in dimension larger than two. In particular, we give their first-order… Expand

Existence and properties of travelling waves for the Gross-Pitaevskii equation

- Fabrice B'ethuel, Philippe Gravejat, J. Saut
- Mathematics
- 1 December 2008

This paper presents recent results concerning the existence and qualitative properties of travelling wave solutions to the Gross-Pitaevskii equation posed on the whole space R^N. Unlike the… Expand

Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation

- Fabrice B'ethuel, Philippe Gravejat, D. Smets
- Mathematics, Physics
- 20 December 2012

We pursue our work on the dynamical stability of dark solitons for the one-dimensional Gross-Pitaevskii equation. In this paper, we prove their asymptotic stability under small perturbations in the… Expand

Decay for travelling waves in the Gross–Pitaevskii equation

- Philippe Gravejat
- Mathematics
- 1 September 2004

Abstract We study the limit at infinity of the travelling waves of finite energy in the Gross–Pitaevskii equation in dimension larger than two: their uniform convergence to a constant of modulus one… Expand

A Non-Existence Result for Supersonic Travelling Waves in the Gross-Pitaevskii Equation

- Philippe Gravejat
- Physics
- 17 October 2003

AbstractWe prove the non-existence of non-constant travelling waves of finite energy and of speed ${{c > \sqrt{{2}}}}$ in the Gross-Pitaevskii equation in dimension N≥2.

On the Korteweg–de Vries Long-Wave Approximation of the Gross–Pitaevskii Equation II

- F. Béthuel, Philippe Gravejat, J. Saut, D. Smets
- Mathematics
- 27 March 2009

In this paper, we proceed along our analysis of the Korteweg–de Vries approximation of the Gross–Pitaevskii equation initiated in [6]. At the long-wave limit, we establish that solutions of small… Expand

Smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation

- Philippe Gravejat, D. Smets
- Mathematics, Physics
- 19 May 2017

We construct families of smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation (SQG). These solutions can be viewed as the equivalents for this equation of the vortex… Expand

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