\(N\)-fold Darboux transformation and double-Wronskian-typed solitonic structures for a variable-coefficient modified Kortweg-de Vries equation

DOI10.1016/j.aop.2012.04.009zbMath1268.37085OpenAlexW2052406102MaRDI QIDQ1758486

Feng-Hua Qi, Lei Wang, Yi-Tian Gao

Publication date: 9 November 2012

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

Full work available at URL: https://doi.org/10.1016/j.aop.2012.04.009

zbMATH Keywords

\(N\)-fold Darboux transformationdouble Wronskian solutionmulti-solitonic solutionsvariable-coefficient modified Korteweg-de Vries model

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

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Cites Work

• Unnamed Item
• Unnamed Item
• Wronskian determinant solutions of the \((3+1)\)-dimensional Jimbo-Miwa equation
• Linear superposition principle applying to Hirota bilinear equations
• Symbolic computation on cylindrical-modified dust-ion-acoustic nebulons in dusty plasmas
• A transformed rational function method and exact solutions to the \(3+1\) dimensional Jimbo-Miwa equation
• Variable-coefficient higher-order nonlinear Schrödinger model in optical fibers: variable-coefficient bilinear form, Bäcklund transformation, Brightons and symbolic computation
• Generalized double Wronskian solutions of the third-order isospectral AKNS equation
• Multisoliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Schrödinger equation from plasma physics, arterial mechanics, fluid dynamics and optical communications
• Analytical study of the nonlinear Schrödinger equation with an arbitrary linear time-dependent potential in quasi-one-dimensional Bose-Einstein condensates
• Transformations for a generalized variable-coefficient Korteweg-de Vries model from blood vessels, Bose-Einstein condensates, rods and positons with symbolic computation
• Solution of a nonisospectral and variable coefficient Korteweg-de Vries equation
• KdV dynamics in the plasma-sheath transition.
• Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications
• New double Wronskian solutions of the AKNS equation
• Dust-ion-acoustic solitary waves in a hot magnetized dusty plasma with charge fluctuations
• Complexiton solutions of the Korteweg-de Vries equation with self-consistent sources
• The modified KdV equation with variable coefficients: Exact uni/bi-variable travelling wave-like solutions
• On the coherent structures of the Nizhnik-Novikov-Veselov equation
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• A Unified Explicit Construction of 2 N -Soliton Solutions for Evolution Equations Determined by 2 × 2 AKNS System
• Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation
• THE DOUBLE WRONSKIAN SOLUTIONS TO THE KADOMTSET–PETVIASHVILI EQUATION
• The Painlevé property for partial differential equations
• On interfacial solitary waves over slowly varying topography
• Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP Equations
• Parametrically controlling solitary wave dynamics in the modified Korteweg-de Vries equation
• Exact Solutions for the Nonisospectral Kadomtshev–Petviashvili Equation

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