Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations

Stefan Le Coz; Tai-Peng Tsai

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arXiv · 1309.7846

Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations

Stefan Le Coz·Tai-Peng Tsai

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Abstract

We look for solutions to generic nonlinear Schrödinger equations build upon solitons and kinks. Solitons are localized solitary waves and kinks are their non localized counter-parts. We prove the existence of infinite soliton trains, i.e. solutions behaving at large time as the sum of infinitely many solitons. We also show that one can attach a kink at one end of the train. Our proofs proceed by fixed point arguments around the desired profile. We present two approaches leading to different results, one based on a combination of dispersive estimates and Strichartz estimates, the other based only on Strichartz estimates.

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Stefan Le Coz, Tai-Peng Tsai. 2013-09-30. Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations. https://arxiv.org/abs/1309.7846

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