Darboux transformation and classification of solution for mixed coupled nonlinear Schr\"odinger equations

TL;DR

This paper develops a unified Darboux transformation approach to derive and classify solutions of mixed coupled nonlinear Schrödinger equations, including solitons, breathers, and rogue waves, on nonzero backgrounds.

Contribution

It introduces a generalized solution formula for mCNLSE and classifies solutions based on their dynamical behavior, detailing conditions for various localized wave phenomena.

Findings

Derived generalized solution formulas for mCNLSE

Classified solutions into solitons, breathers, and rogue waves

Analyzed interactions between different localized wave solutions

Abstract

We derive generalized nonlinear wave solution formula for mixed coupled nonlinear Sch\"odinger equations (mCNLSE) by performing the unified Darboux transformation. We give the classification of the general soliton formula on the nonzero background based on the dynamical behavior. Especially, the conditions for breather, dark soliton and rogue wave solution for mCNLSE are given in detail. Moreover, we analysis the interaction between dark-dark soliton solution and breather solution. These results would be helpful for nonlinear localized wave excitations and applications in vector nonlinear systems.