Bäcklund transformation classification, integrability and exact solutions to the generalized Burgers'-KdV equation

DOI10.1016/J.CNSNS.2016.07.022zbMath1465.37079OpenAlexW2495524207MaRDI QIDQ2005025

Hanze Liu, Zenggui Wang, Xi-Qiang Liu, Xiang-Peng Xin

Publication date: 7 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2016.07.022

zbMATH Keywords

exact solutionintegrabilitydirect methodBäcklund transformationhomogeneous balance principle

Mathematics Subject Classification ID

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) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Solutions to PDEs in closed form (35C05)

Related Items (7)

Equivalence transformation, dynamical analysis and exact solutions of Harry-Dym system with variable coefficients ⋮ Burgers' equations in the Riemannian geometry associated with first-order differential equations ⋮ Non-auto Bäcklund transformation, nonlocal symmetry and CRE solvability for the Bogoyavlenskii-Kadomtsev-Petviashvili equation ⋮ An analytic approach to constructing Bäcklund transformations and exact solutions to nonlinear wave equations in non-polynomial form ⋮ Painlevé test, complete symmetry classifications and exact solutions to R-D types of equations ⋮ Symmetry reductions, dynamical behavior and exact explicit solutions to a class of nonlinear shallow water wave equation ⋮ Lie symmetry analysis, bifurcations and exact solutions for the (2+1)-dimensional dissipative long wave system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Painlevé analysis, \({\Phi}\)-integrable and exact solutions to the \((3+1)\)-dimensional nonlinear evolution equations
• Painlevé analysis, complete Lie group classifications and exact solutions to the time-dependent coefficients gardner types of equations
• Generalized symmetry classifications, integrable properties and exact solutions to the general nonlinear diffusion equations
• Painlevé test, generalized symmetries, Bäcklund transformations and exact solutions to the third-order Burgers' equations
• Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
• Darboux transformations in integrable systems. Theory and their applications to geometry
• The Painlevé property for partial differential equations
• Nonlinear wave motion governed by the modified Burgers equation
• Parametric Bäcklund transformations I: Phenomenology
• Symmetries and differential equations
• A new Bäcklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients

This page was built for publication: Bäcklund transformation classification, integrability and exact solutions to the generalized Burgers'-KdV equation