Finite and infinite soliton and kink-soliton trains of nonlinear Schr\"odinger equations

Stefan Le Coz; Tai-Peng Tsai

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arXiv · 1409.8379

Finite and infinite soliton and kink-soliton trains of nonlinear Schr\"odinger equations

Stefan Le Coz·Tai-Peng Tsai

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Abstract

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 Schr\"odinger 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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Stefan Le Coz, Tai-Peng Tsai. 2014-09-30. Finite and infinite soliton and kink-soliton trains of nonlinear Schr\"odinger equations. https://arxiv.org/abs/1409.8379

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