High speed excited multi-solitons in nonlinear Schrödinger equations

Raphaël Côte (1) , Stefan Le Coz (2)

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

We consider the nonlinear Schrödinger equation with a general nonlinearity. In dimension higher than 2, this equation admits travelling wave solutions with a fixed profile which is not the ground state. This kind of profiles are called excited states. In this paper, we construct solutions to NLS behaving like a sum of N excited states which spread up quickly as time grows (which we call multi-solitons). We also show that if the flow around one of these excited states is linearly unstable, then the multi-soliton is not unique, and is unstable.

Mots clés: multi-solitons; nonlinear Schrödinger equations; excited states

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Côte, Stefan Le Coz. High speed excited multi-solitons in nonlinear Schrödinger equations. Journal de Mathématiques Pures et Appliquées, 2011, 96 (2), http://dx.doi.org/10.1016/j.matpur.2011.03.004. ⟨10.1016/j.matpur.2011.03.004⟩. ⟨hal-00503279v2⟩