Orbital stability of the black soliton to the Gross-Pitaevskii equation
  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. 
Fabrice B\'ethuel (LJLL), Philippe Gravejat (CEREMADE), Jean-Claude   Saut (LM-Orsay), Didier Smets (LJLL)