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

Didier Smets (LJLL); Fabrice B\'ethuel (LJLL); Jean-Claude Saut (LM-Orsay); Philippe Gravejat (CEREMADE)

arxiv: 0804.0746 · v2 · submitted 2008-04-04 · 🧮 math.AP

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

Fabrice B\'ethuel (LJLL) , Philippe Gravejat (CEREMADE) , Jean-Claude Saut (LM-Orsay) , Didier Smets (LJLL) This is my paper

classification 🧮 math.AP

keywords blackequationgross-pitaevskiiorbitalsolitonstabilityenergyestablish

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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 perturbations in the energy space.

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

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