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

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.

Final version published in Indiana University Mathematics Journal

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• Exotic traveling waves for a quasilinear Schrödinger equation with nonzero background
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