61 citations · 63 across the 3 of their papers we have counts for
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Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation
Fabrice Béthuel, Philippe Gravejat, Didier Smets
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 per…
Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
Fabrice Béthuel, Philippe Gravejat, Didier Smets
We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero,…
Existence and properties of travelling waves for the Gross-Pitaevskii equation
Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut
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. U…
On the KP I transonic limit of two-dimensional Gross-Pitaevskii travelling waves
Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut
We provide a rigorous mathematical derivation of the convergence in the long-wave transonic limit of the minimizing travelling waves for the two-dimensional Gross-Pitaevskii equati…
Orbital stability of the black soliton to the Gross-Pitaevskii equation
Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut +1
We establish the orbital stability of the black soliton, or kink solution, $\v_0(x) = þ\big(\frac{x}{\sqrt{2}} \big)$, to the one-dimensional Gross-Pitaevskii equation, with respec…