Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation

DOI10.1063/1.4732464zbMath1276.81068OpenAlexW2059930629MaRDI QIDQ2865522

Liming Ling, Bo-ling Guo

Publication date: 29 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/4086c8c03e9e72f9dba2c05bf9ed1dcfeea757cc

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Groups and algebras in quantum theory and relations with integrable systems (81R12) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08)

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Cites Work

• Unnamed Item
• Dressing for a novel integrable generalization of the nonlinear Schrödinger equation
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Perturbation theory for the modified nonlinear Schrödinger solitons
• New integrable systems of derivative nonlinear Schrödinger equations with multiple components
• Lattice representation and dark solitons of the Fokas–Lenells equation
• Darboux transformation for a two-component derivative nonlinear Schrödinger equation
• An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons
• Alfvén solitons in the coupled derivative nonlinear Schrödinger system with symbolic computation
• An exact solution for a derivative nonlinear Schrödinger equation
• The hierarchy of multi-soliton solutions of the derivative nonlinear Schr dinger equation
• The Two Component Derivative Nonlinear Schrodinger Equation
• Generalization of the Kaup-Newell Inverse Scattering Formulation and Darboux Transformation
• Integrable Multi-Component Hybrid Nonlinear Schrödinger Equations
• Gauge Transformations among Generalised Nonlinear Schrödinger Equations
• Complete integrability of derivative nonlinear Schrödinger-type equations
• On a novel integrable generalization of the nonlinear Schrödinger equation

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