Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations

2013/09/30 by Stefan Le Coz, Tai‐Peng Tsai, Coz, Stefan Le +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1309.7846

openalex publication_date 2013/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Uniqueness of positive solutions of Δu−u+up=0 in Rn
• Nonlinear scalar field equations, II existence of infinitely many solutions
• Orbital stability of standing waves for some nonlinear Schr�dinger equations
• Nonlinear Schr�dinger equations and sharp interpolation estimates
• Nonlinear scalar field equations, I existence of a ground state

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