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arXiv · 0804.0746

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

Fabrice Béthuel·Philippe Gravejat·Jean-Claude Saut·Didier Smets
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Abstract

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 respect to perturbations in the energy space.

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Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut, Didier Smets. 2009-02-09. Orbital stability of the black soliton to the Gross-Pitaevskii equation. https://doi.org/10.1512/iumj.2008.57.3632

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