The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation
type: Item
instance of: scholarly article
title: The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation
zbMATH Open document ID: 1412.35380
author: Wen-Xiu Ma
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-12-20T00:00:00Z
review text: The author considers a combined modified Korteweg-de Vries (mKdV) equation and its inverse scattering transform in terms of the Riemann-Hilbert problems. Soliton solutions are computed to the combined mKdV equation from special associated Riemann-Hilbert problems on the real axis by taking the jump matrix as the identity matrix.
reviewed by: Ti-Jun Xiao
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 6996209
zbMATH Keywords: inverse scattering transform
zbMATH Keywords: Riemann-Hilbert problem
zbMATH Keywords: soliton solution
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.11.014
OpenAlex ID: W2900441300
cites work: The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
cites work: Q3925229
cites work: Q4303160
cites work: A dressing method in mathematical physics.
cites work: Generalized fractional supertrace identity for Hamiltonian structure of NLS-MKdV hierarchy with self-consistent sources
cites work: Generalised (2+1)-dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory
cites work: Q3658448
cites work: The unified method. I: Nonlinearizable problems on the half-line
cites work: Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique
cites work: Riemann-Hilbert approach and \(N\)-soliton solutions for a generalized Sasa-Satsuma equation
cites work: Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy
cites work: Q5701874
cites work: Integrable Hamiltonian hierarchies. Spectral and geometric methods
cites work: Q4423191
cites work: Q4828547
cites work: Q4788856
cites work: Q3344588
cites work: Integrals of nonlinear equations of evolution and solitary waves
cites work: The unified method. III: Nonlinearizable problems on the interval
cites work: A nonconfocal involutive system and constrained flows associated with the MKdV− equation
cites work: Q4016078
cites work: Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
cites work: The algebraic structures of isospectral Lax operators and applications to integrable equations
cites work: The algebraic structure of zero curvature representations and application to coupled KdV systems
cites work: Complexiton solutions to the Korteweg-de Vries equation
cites work: Trigonal curves and algebro-geometric solutions to soliton hierarchies I
cites work: Trigonal curves and algebro-geometric solutions to soliton hierarchies II
cites work: Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
cites work: Semi-direct sums of Lie algebras and continuous integrable couplings
cites work: Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
cites work: Darboux transformations of integrable couplings and applications
cites work: Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations
cites work: Q4002235
cites work: Q3732103
cites work: Evolution equations possessing infinitely many symmetries
cites work: Two-dimensional lumps in nonlinear dispersive systems
cites work: Perturbation theory for nearly integrable multicomponent nonlinear PDEs
cites work: General soliton matrices in the Riemann–Hilbert problem for integrable nonlinear equations
cites work: The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
cites work: Integrable properties of the general coupled nonlinear Schrödinger equations
cites work: Binary nonlinearization for AKNS-KN coupling system
cites work: Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation
cites work: A Riemann-Hilbert approach to the Harry-Dym equation on the line
cites work: An integrable coupling hierarchy of the MKdV\_integrable systems, its Hamiltonian structure and corresponding nonisospectral integrable hierarchy
cites work: Nonlinear Waves in Integrable and Nonintegrable Systems
cites work: Rational solutions and lump solutions to the generalized \((3+1)\)-dimensional shallow water-like equation
Wikidata QID: Q128911057
DOI: 10.1016/J.JMAA.2018.11.014
description: scientific article; zbMATH DE number 6996209