Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations

Abstract

We derive generalized nonlinear wave solution formula for mixed coupled nonlinear Schödinger 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.

28 pages, 9 figures

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Cited by in corpus (13)

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• Higher-order vector Peregrine solitons and asymptotic estimates for the multi-component nonlinear Schrödinger equations
• Darboux transformation of nonisospectral coupled Gross-Pitaevskii equation and its multi-component generalization
• The Mechanism of Kuznetsov-Ma Breather
• High-order rogue waves of a long wave-short wave model
• Comment on "Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations"
• General soliton solutions to a coupled Fokas-Lenells equation
• Generalized Darboux transformation and higher-order rogue wave solutions of the coupled Hirota equations
• Reply to "Comment on "Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations""
• Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger system and its soliton solutions
• Nondegenerate bright solitons in coupled nonlinear Schrödinger systems: Recent developments on optical vector solitons
• A General Integrable Nonlocal Coupled Nonlinear Schrödinger Equation