CK transformations, symmetries, exact solutions and conservation laws of the generalized variable-coefficient KdV types of equations

DOI10.1016/j.cam.2018.06.019zbMath1405.37080OpenAlexW2808849249WikidataQ129622005 ScholiaQ129622005MaRDI QIDQ1789692

Bo Sang, Hanze Liu, Xiang-Peng Xin, Xi-Qiang Liu

Publication date: 10 October 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.06.019

zbMATH Keywords

exact solutionconservation lawvariable-coefficient equationLie group classificationCK transformation

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)

Related Items (12)

Equivalent transformations, bifurcations and exact solutions to a class of variable-coefficient PDE ⋮ Equivalence transformation, dynamical analysis and exact solutions of Harry-Dym system with variable coefficients ⋮ Bäcklund transformations, symmetry reductions and exact solutions of (2+1)-dimensional nonlocal DS equations ⋮ Invariant subspace classification and exact explicit solutions to a class of nonlinear wave equation ⋮ Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients ⋮ Painlevé test, complete symmetry classifications and exact solutions to R-D types of equations ⋮ Equivalent transformations and exact solutions to the generalized cylindrical KdV type of equation ⋮ Improved equivalent transformation method for reduction NLPDEs with time-dependent variables ⋮ A novel Lie group classification method for generalized cylindrical KdV type of equation: exact solutions and conservation laws ⋮ Lie symmetry, nonlocal symmetry analysis, and interaction of solutions of a \((2+1)\)-dimensional KdV-mKdV equation ⋮ Symmetry reductions, dynamical behavior and exact explicit solutions to a class of nonlinear shallow water wave equation ⋮ Lie symmetry analysis of (2+1)-dimensional KdV equations with variable coefficients

Cites Work

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• Decay mode solutions to cylindrical KP equation
• Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping
• New explicit solutions of the fifth-order KdV equation with variable coefficients
• Painlevé analysis, auto-Bäcklund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation
• Symmetry and integration methods for differential equations
• Lie symmetries, integrable properties and exact solutions to the variable-coefficient nonlinear evolution equations
• Conservation laws and non-invariant solutions of anisotropic wave equations with a source
• Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid
• Lax pair, auto-Bäcklund transformation and conservation law for a generalized variable-coefficient KdV equation with external-force term
• Periodic and solitary wave solutions for a generalized variable-coefficient Boiti-Leon-Pempinlli system
• Invariant subspaces and conditional Lie-Bäcklund symmetries of inhomogeneous nonlinear diffusion equations
• The exact solution and integrable properties to the variable-coefficient modified Korteweg-de Vries equation
• New similarity reductions of the Boussinesq equation
• The Painlevé property for partial differential equations
• A variable coefficient Korteweg–de Vries equation: Similarity analysis and exact solution. II
• Non-Lie symmetry groups of (2+1)-dimensional nonlinear systems obtained from a simple direct method

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