The Riemann-Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient \((2+1)\)-dimensional KdV equation

DOI10.1007/s11071-016-3219-xzbMath1373.37165OpenAlexW2554180454MaRDI QIDQ1673973

Zhonglong Zhao, Bo Han

Publication date: 27 October 2017

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-016-3219-x

zbMATH Keywords

soliton solutionsBäcklund transformationa generalized variable coefficient \((2+1)\)-dimensional Korteweg-de Vries equationquasiperiodic wave solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)

Related Items (5)

Residual symmetry, Bäcklund transformation and CRE solvability of a \((2+1)\)-dimensional nonlinear system ⋮ Application of the Riemann-Hilbert method to the vector modified Korteweg-de Vries equation ⋮ Conservation laws and nonlocally related systems of the Hunter-Saxton equation for liquid crystal ⋮ Approximate symmetries, conservation laws and numerical solutions for a class of perturbed linear wave type system ⋮ Nonlocal symmetry and similarity reductions for a \((2+1)\)-dimensional Korteweg-de Vries equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Breathers and localized solitons for the Hirota-Maxwell-Bloch system on constant backgrounds in erbium doped fibers
• Breather-to-soliton conversions and nonlinear wave interactions in a coupled Hirota system
• Soliton and Riemann theta function quasi-periodic wave solutions for a \((2+1)\)-dimensional generalized shallow water wave equation
• Bäcklund transformations and soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries-type equation in water waves
• Lump solutions to dimensionally reduced \(p\)-gKP and \(p\)-gBKP equations
• Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation
• The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials
• Generalized (2 + 1)-dimensional Gardner model: bilinear equations, Bäcklund transformation, Lax representation and interaction mechanisms
• On a direct procedure for the quasi-periodic wave solutions of the supersymmetric Ito's equation
• Supersymmetric KdV-Sawada-Kotera-Ramani equation and its quasi-periodic wave solutions
• Symmetry and integration methods for differential equations
• Binary Bell polynomial manipulations on the integrability of a generalized (2+1)-dimensional Korteweg-de Vries equation
• Lump solutions to the Kadomtsev-Petviashvili equation
• Uncertainty principle for the nonlinear waves of the Korteweg-de Vries equation
• Breathers and multi-soliton solutions for the higher-order generalized nonlinear Schrödinger equation
• New bilinear Bäcklund transformation with multisoliton solutions for the (2+1)-dimensional Sawada-Kotera model
• The investigation into the Schwarz–Korteweg–de Vries equation and the Schwarz derivative in (2+1) dimensions
• Simple Derivation of Backlund Transformation from Riccati Form of Inverse Method
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Bäcklund transformation and special solutions for the Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations
• A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
• A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. II. Exact One- and Two-Periodic Wave Solution of the Coupled Bilinear Equations
• Super extension of Bell polynomials with applications to supersymmetric equations
• Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform
• A New (2 + 1)-Dimensional KdV Equation and Its Localized Structures
• EXACT ONE-PERIODIC AND TWO-PERIODIC WAVE SOLUTIONS TO HIROTA BILINEAR EQUATIONS IN (2+1) DIMENSIONS
• Bäcklund transformations, soliton solutions and wave functions of Kaup–Newell and Wadati–Konno–Ichikawa systems
• Quasi-periodic waves and an asymptotic property for the asymmetrical Nizhnik–Novikov–Veselov equation
• Inverse scattering theory of the heat equation for a perturbed one-soliton potential
• Darboux covariant Lax pairs and infinite conservation laws of the (2+1)-dimensional breaking soliton equation
• Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices

This page was built for publication: The Riemann-Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient \((2+1)\)-dimensional KdV equation