Finite and infinite soliton and kink-soliton trains of nonlinear Schrödinger equations

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

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

We will first review known results on multi-solitons of dispersive partial differential equations, which are special solutions behaving like the sum of many weakly-interacting solitary waves. We will then describe our recent joint work with Dong Li on nonlinear Schrödinger equations: 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. In the 1D case, we can add to the infinite train an additional half-kink, which is a solution with a non-zero background at minus infinity.

Mots clés: infinite soliton train; nonlinear Schrödinger equation; soliton; multi-soliton; kink-soliton train

Domaines: Equations aux dérivées partielles [math.AP]

Stefan Le Coz, Tai-Peng Tsai. Finite and infinite soliton and kink-soliton trains of nonlinear Schrödinger equations. Proceedings of the Sixth International Congress of Chinese Mathematicians. Vol. I, 2013, Taipei, Taiwan. pp.43-56. ⟨hal-01069822v2⟩