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 study *infinite soliton trains* solutions of nonlinear Schrödinger equations (NLS), i.e. solutions behaving at large time as the sum of infinitely many solitary waves. Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of such a soliton train. We also give a new construction of multi-solitons (i.e. finite trains) and prove uniqueness in an exponentially small neighborhood, and we consider the case of solutions composed of several solitons and 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. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2015, 145 (6), pp.1251--1282. ⟨10.1017/S030821051500030X⟩. ⟨hal-00811621v3⟩