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

Mathematics – Analysis of PDEs

Scientific paper

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Final version published in Indiana University Mathematics Journal

Scientific paper

10.1512/iumj.2008.57.3632

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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