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Pré-Publication, Document De Travail Année : 2014

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

Résumé

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.
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Dates et versions

hal-01069822 , version 1 (30-09-2014)
hal-01069822 , version 2 (11-04-2016)

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Stefan Le Coz, Tai-Peng Tsai. Finite and infinite soliton and kink-soliton trains of nonlinear Schrödinger equations. 2014. ⟨hal-01069822v1⟩
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