Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations

DOI10.1016/j.geomphys.2020.103845zbMath1452.37069OpenAlexW3047889030MaRDI QIDQ2201724

Wen-Xiu Ma

Publication date: 17 September 2020

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2020.103845

zbMATH Keywords

inverse scattering transformRiemann-Hilbert problemsoliton solutionmatrix spectral problemnonlocal integrable equationreverse space-time

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (12)

Inverse scattering transforms for the nonlocal Hirota–Maxwell–Bloch system ⋮ \( \overline{\partial} \)-dressing method for the nonlocal mKdV equation ⋮ Field and reverse field solitons in wave-operator nonlinear Schrödinger equation with space-time reverse: Modulation instability ⋮ Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation ⋮ On the Cauchy problem for the mKdV-sine-Gordon equation with an additional term ⋮ Kinky breather-wave and lump solutions to the \((2+1)\)-dimensional Burgers equations ⋮ The ∂̄-dressing method and soliton solutions for the three-component coupled Hirota equations ⋮ Spectral and soliton structures of the Sasa-Satsuma higher-order nonlinear Schrödinger equation ⋮ The soliton solutions and long-time asymptotic analysis for an integrable variable coefficient nonlocal nonlinear Schrödinger equation ⋮ \(N\)-soliton, \(M\)-breather and hybrid solutions of a time-dependent Kadomtsev-Petviashvili equation ⋮ Riemann-Hilbert problems and inverse scattering of nonlocal real reverse-spacetime matrix AKNS hierarchies ⋮ Riemann-Hilbert approach for the Kundu equation with non-vanishing boundary conditions: simple and double poles

Cites Work

• A Riemann-Hilbert approach to the Harry-Dym equation on the line
• General \(N\)-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
• A dressing method in mathematical physics.
• Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
• Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces
• Adjoint symmetry constraints of multicomponent AKNS equations.
• On a nonlocal modified Korteweg-de Vries equation: integrability, Darboux transformation and soliton solutions
• Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrödinger equation
• Rational solutions and lump solutions to the generalized \((3+1)\)-dimensional shallow water-like equation
• Long-time asymptotics of a three-component coupled nonlinear Schrödinger system
• Riemann-Hilbert approach and \(N\)-soliton solutions for a generalized Sasa-Satsuma equation
• Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform
• Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions
• Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Trigonal curves and algebro-geometric solutions to soliton hierarchies I
• Nonlocal nonlinear Schrödinger equations and their soliton solutions
• Integrable Nonlocal Nonlinear Equations
• Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation
• Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
• Integrable properties of the general coupled nonlinear Schrödinger equations
• Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations