Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions

2011/06/01 by Caroline Kalla, Kalla, Caroline · 1 citation
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1106.0154

arxiv created 2011/06/01 · openalex publication_date 2011/06/01 · arxiv updated 2011/06/02 · openalex created_date 2022/08/14 · openalex updated_date 2026/07/28

Abstract

We present new solutions in terms of elementary functions of the multi-component nonlinear Schrödinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular we present for the first time breather and rational breather solutions of the multi-component nonlinear Schrödinger equations.

Cited by

• KP solitons and the Schottky uniformization

Related

• Two-component breather solution of the nonlinear wave equation
• Explicit breather solution of the nonlinear Schrödinger equation
• About the corollaries of the soliton-breather models of particles tunneling on the example of the nonlinear Klein-Gordon and Schrodinger equation
• Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation
• Dark solitons, Breathers and Rogue Wave Solutions of the Coupled Generalized Nonlinear Schrödinger Equations