Asymptotic stability of the black soliton for the Gross-Pitaevskii equation

Philippe Gravejat (1) , Didier Smets (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions

We introduce a new framework for the analysis of the stability of solitons for the one-dimensional Gross-Pitaevskii equation. In particular, we establish the asymptotic stability of the black soliton with zero speed.

Mots clés: asymptotic stability.; solitons; asymptotic stability; Gross-Pitaevskii equation

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Gravejat, Didier Smets. Asymptotic stability of the black soliton for the Gross-Pitaevskii equation. Proceedings of the London Mathematical Society, 2015, 111 (2), pp.305-353. ⟨10.1112/plms/pdv025⟩. ⟨hal-01002094⟩