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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218807We 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 JournalAnalysis of PDEs35B35, 35Q40, 35Q55Orbital stability of the black soliton to the Gross-Pitaevskii equationtext