Breathers and solitons of generalized nonlinear Schr\"odinger equations as degenerations of algebro-geometric solutions

TL;DR

This paper derives new breather and soliton solutions for multi-component nonlinear Schr"odinger equations by degenerating algebro-geometric solutions, including the first known rational breather solutions.

Contribution

It introduces a simple determinantal form for these solutions and presents the first breather and rational breather solutions for multi-component nonlinear Schr"odinger equations.

Findings

New breather and soliton solutions derived

Solutions expressed in simple determinantal form

First known rational breather solutions for these equations

Abstract

We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger 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 Schr\"odinger equations.