Symmetry classification of KdV-type nonlinear evolution equations

DOI10.1063/1.1737811zbMath1071.35112arXivnlin/0201063OpenAlexW3102188242MaRDI QIDQ4833424

V. I. Lahno, F. Güngör, Renat Zhdanov

Publication date: 15 December 2004

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

Full work available at URL: https://arxiv.org/abs/nlin/0201063

zbMATH Keywords

Lie algebranonlinear evolution equationequivalence groupequivalence transformationsymmetry classificationthird-order equationsrealisationLevi decompositioninvariance algebraKdV type equation

Mathematics Subject Classification ID

Related Items (37)

Mapping method of group classification ⋮ Symmetry classification of quasi-linear PDE's containing arbitrary functions ⋮ A family of wave equations with some remarkable properties ⋮ Lie group analysis of a generalized Krichever-Novikov differential-difference equation ⋮ Group classification and conservation laws of a class of hyperbolic equations ⋮ A symmetry classification algorithm of the generalized differential-difference equations ⋮ Comment on ``Group analysis of KdV equation with time dependent coefficients ⋮ Two approximate symmetry frameworks for nonlinear partial differential equations with a small parameter: Comparisons, relations, approximate solutions ⋮ Lie group classification of the \(N\)-th-order nonlinear evolution equations ⋮ Equivalence groupoid of a class of variable coefficient Korteweg–de Vries equations ⋮ Linearizability for third order evolution equations ⋮ Group analysis of general Burgers–Korteweg–de Vries equations ⋮ Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations ⋮ Group classification of linear fourth-order evolution equations ⋮ Abelian Lie symmetry algebras of two‐dimensional quasilinear evolution equations ⋮ Symmetry classification of third-order nonlinear evolution equations. I: Semi-simple algebras ⋮ Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach ⋮ Group classification and exact solutions of a class of nonlinear waves ⋮ Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations ⋮ Nonlinear self-adjoint classification of a Burgers-KdV family of equations ⋮ Symmetry reduction and soliton-like solutions for the generalized Korteweg-de Vries equation ⋮ Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations ⋮ Numerical analytic method for solving a large class of generalized non-homogeneous variable coefficients KdV problems based on lie symmetries ⋮ Self-adjoint sub-classes of third and fourth-order evolution equations ⋮ Group classification of differential-difference equations: low-dimensional Lie algebras ⋮ Algorithmic symmetry classification with invariance ⋮ Classification of local and nonlocal symmetries of fourth-order nonlinear evolution equations ⋮ Symmetry groups of differential-difference equations and their compatibility ⋮ Galilei symmetries of KdV-type nonlinear evolution equations ⋮ More common errors in finding exact solutions of nonlinear differential equations. I ⋮ Group classification of linear evolution equations ⋮ On the existence of conservation law multiplier for partial differential equations ⋮ Time-dependent exact solutions for Rosenau-Hyman equations with variable coefficients ⋮ Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries ⋮ Preliminary group classification of quasilinear third-order evolution equations ⋮ Preliminary group classification of a class of fourth-order evolution equations ⋮ Infinite-dimensional symmetries of two-dimensional generalized Burgers equations

Cites Work

• Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra
• New scale-invariant nonlinear differential equations for a complex scalar field
• Symmetry classification of diatomic molecular chains
• The evolution partial differential equation u t=u x x x+3(u x x u2 +3u2x u)+3u x u4
• Low-dimensional real Lie algebras
• A symmetry approach to exactly solvable evolution equations
• Invariants of real low dimension Lie algebras
• Group classification of heat conductivity equations with a nonlinear source
• Symmetries of variable coefficient Korteweg–de Vries equations
• Symmetries of discrete dynamical systems involving two species
• Symmetries of discrete dynamical systems
• Lie symmetries versus integrability in evolution equations
• Symmetry classes of variable coefficient nonlinear Schrodinger equations
• On preliminary symmetry classification of nonlinear Schrödinger equations with some applications to Doebner-Goldin models
• The structure of Lie algebras and the classification problem for partial differential equations

This page was built for publication: Symmetry classification of KdV-type nonlinear evolution equations