On the determining equations for the nonclassical reductions of the heat and Burgers' equation

DOI10.1016/S0022-247X(02)00091-4zbMath1009.35005MaRDI QIDQ1614709

Fred Hickling, Daniel J. Arrigo

Publication date: 8 September 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Hopf-Cole transformationnonclassical symmetrygroup analysis methods

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Invariance and symmetry properties for PDEs on manifolds (58J70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Geometric theory, characteristics, transformations in context of PDEs (35A30) Symmetries of infinite-dimensional dissipative dynamical systems (37L20)

Related Items (7)

Reduction operators and exact solutions of generalized Burgers equations ⋮ New conditional symmetries and exact solutions of reaction-diffusion-convection equations with exponential nonlinearities ⋮ Extended symmetry analysis of generalized Burgers equations ⋮ Nonclassical symmetries of evolutionary partial differential equations and compatibility. ⋮ Reduction operators of Burgers equation ⋮ Nonclassical symmetries of a class of Burgers' systems ⋮ Singular reduction modules of differential equations

Cites Work

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• The nonclassical group analysis of the heat equation
• All solutions of standard symmetric linear partial differential equations have classical Lie symmetry
• Symmetry reductions and exact solutions of a class of nonlinear heat equations
• Nonclassical solutions are non-existent for the heat equation and rare for nonlinear diffusion
• Non-classical symmetry reduction: example of the Boussinesq equation
• Nonclassical symmetry solutions and the methods of Bluman–Cole and Clarkson–Kruskal
• Nonclassical symmetry reductions of the linear diffusion equation with a nonlinear source
• Nonlinear boundary value problems in science and engineering
• Symmetries and differential equations

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