Multi-Speeds solitary waves solutions for nonlinear Schrödinger systems

Isabella Ianni (1) , Stefan Le Coz (2)

1 Dipartimento di Matematica
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove the existence of a new type of solutions to a nonlinear Schrödinger system. These solutions, which we call "multi-speeds solitary waves", are behaving at large time as a couple of scalar solitary waves traveling at different speeds. The proof relies on the construction of approximations of the multi-speeds solitary waves by solving the system backwards in time and using energy methods to obtain uniform estimates.

Mots clés: solitary waves; nonlinear Schrödinger systems

Domaines: Equations aux dérivées partielles [math.AP]

Isabella Ianni, Stefan Le Coz. Multi-Speeds solitary waves solutions for nonlinear Schrödinger systems. Journal of the London Mathematical Society, 2014, 89 (2), pp.623-639. ⟨10.1112/jlms/jdt083⟩. ⟨hal-00688563v2⟩