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math.AP2008★ 61 cited
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…
math.AP2007★ 133 cited
Travelling waves for the Gross-Pitaevskii equation II
Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut
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. Ou…