New exact explicit solutions of the generalized KdV equations

DOI10.1016/j.amc.2008.03.013zbMath1158.35420OpenAlexW2079466856MaRDI QIDQ942393

D. Pandiaraja, B. Mayil Vaganan, M. Senthil Kumaran

Publication date: 5 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2008.03.013

zbMATH Keywords

similarity solutionLie group methodEuler-Painlevé equationsgeneralized KdV equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Solutions to PDEs in closed form (35C05)

Related Items (12)

Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients ⋮ Topological 1-soliton solution of the generalized KdV equation with generalized evolution ⋮ Constructing of new exact solutions to the GKdV-mKdV equation with any-order nonlinear terms by \((\frac{G'}{G})\)-expansion method ⋮ Group method solutions of the generalized forms of Burgers, Burgers-KdV and KdV equations with time-dependent variable coefficients ⋮ Constructing of exact solutions to the KdV and Burgers equations with power-law nonlinearity by the extended \((\frac{G'}{G})\)-expansion method ⋮ Exact solutions of KdV equation with time-dependent coefficients ⋮ Solitary wave solution for the generalized KdV equation with time-dependent damping and dispersion ⋮ Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients ⋮ 1-soliton solution of the \(K(m,n)\) equation with generalized evolution and time-dependent damping and dispersion ⋮ Group analysis of KdV equation with time dependent coefficients ⋮ Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries ⋮ Lie symmetry analysis of (2+1)-dimensional KdV equations with variable coefficients

Cites Work

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• The application of bifurcation method to a higher-order KdV equation
• Exact Linearization and Invariant Solutions of the Generalized Burgers Equation with Linear Damping and Variable Viscosity
• Auto-Bäcklund transformation, Lax pairs, and Painlevé property of a variable coefficient Korteweg–de Vries equation. I
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries

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