Orbital stability of the black soliton to the Gross-Pitaevskii equation
arXiv:0804.0746 · doi:10.1512/iumj.2008.57.3632
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