Application of Riemann-Hilbert method to an extended coupled nonlinear Schrödinger equations

DOI10.1016/j.cam.2022.114812zbMath1504.35500OpenAlexW4295854199WikidataQ114201621 ScholiaQ114201621MaRDI QIDQ2087512

Hai-Feng Wang, Yu-Feng Zhang

Publication date: 21 October 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2022.114812

zbMATH Keywords

Riemann-Hilbert problemmulti-soliton solutionsextended coupled nonlinear Schrödinger equationsmulti-component nonlinear Schrödinger system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Scattering theory for PDEs (35P25) Applications of Lie (super)algebras to physics, etc. (17B81) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (5)

Four-component integrable hierarchies and their Hamiltonian structures ⋮ Four-component integrable hierarchies of Hamiltonian equations with \((m+n+2)\)th-order Lax pairs ⋮ Solitons for the coupled matrix nonlinear Schrödinger-type equations and the related Schrödinger flow ⋮ AKNS type reduced integrable bi-Hamiltonian hierarchies with four potentials ⋮ Localized waves solutions for the fifth-order coupled extended modified KdV equation

Cites Work

• Unnamed Item
• Unnamed Item
• Multi-component generalization of the Camassa-Holm equation
• A Riemann-Hilbert approach for the Novikov equation
• Multi-component integrable systems and invariant curve flows in certain geometries
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• Integrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy
• Riemann-Hilbert problems and \(N\)-soliton solutions for a coupled mKdV system
• Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies
• Long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions
• A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system
• A kind of nonisospectral and isospectral integrable couplings and their Hamiltonian systems
• Computational study on the dynamics of fractional order differential equations with applications
• Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions
• Long-time asymptotics of a three-component coupled nonlinear Schrödinger system
• Two integrable couplings of a generalized d-Kaup-Newell hierarchy and their Hamiltonian and bi-Hamiltonian structures
• Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Riemann-Hilbert approach and \(N\)-soliton solutions for a generalized Sasa-Satsuma equation
• Hamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy
• Long-time asymptotics for the spin-1 Gross-Pitaevskii equation
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Gauge transformation and symmetries of the commutative multicomponent BKP hierarchy
• Inverse scattering transform for the Degasperis–Procesi equation
• Method for Solving the Korteweg-deVries Equation
• Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy
• Multicomponent equations associated to non-isospectral scattering problems
• Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling
• A novel kind of AKNS integrable couplings and their Hamiltonian structures
• Affine Weyl group symmetries of Frobenius Painlevé equations
• The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach
• A Riemann–Hilbert approach for the Degasperis–Procesi equation
• The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras

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