Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations

Stefan Le Coz (1) , Dong Li (2) , Tai-Peng Tsai (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UBC - University of British Columbia

We consider the energy-subcritical NLS. A multi-soliton is a special solution to NLS behaving like the sum of many weakly-interacting solitary waves. Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of a soliton train which is a multi-soliton composed of infinitely many solitons. We also give a new construction of multi-solitons and prove uniqueness in an exponentially small neighborhood, and we consider the case of solutions composed of several kinks (i.e. solutions with a non-zero background at infinity).

Mots clés: soliton train; multi-soliton; multi-kink; nonlinear Schrödinger equations

Domaines: Equations aux dérivées partielles [math.AP]

Stefan Le Coz, Dong Li, Tai-Peng Tsai. Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations. 2013. ⟨hal-00811621v1⟩