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Travelling Waves for the Gross-Pitaevskii Equation II
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, basedExpand
Orbital stability of the black soliton to the Gross-Pitaevskii equation
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 toExpand
Asymptotic stability of the black soliton for the Gross–Pitaevskii equation
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 solitonExpand
Asymptotics for the travelling waves in the Gross-Pitaevskii equation
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-orderExpand
Existence and properties of travelling waves for the Gross-Pitaevskii equation
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 theExpand
Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation
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 theExpand
Decay for travelling waves in the Gross–Pitaevskii equation
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 oneExpand
A Non-Existence Result for Supersonic Travelling Waves in the Gross-Pitaevskii Equation
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
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 smallExpand
Smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation
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 vortexExpand
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