Systems of reaction diffusion equations and their symmetry properties

DOI10.1063/1.1331318zbMath1053.35067OpenAlexW2032570183MaRDI QIDQ2774856

Ronald J. Wiltshire, Anatolia G. Nikitin

Publication date: 26 February 2002

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

Full work available at URL: https://doi.org/10.1063/1.1331318

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (11)

Group classification of systems of nonlinear reaction-diffusion equations with general diffusion matrix. I: Generalized Ginzburg-Landau equations ⋮ Conditional Lie-Bäcklund Symmetry of Evolution System and Application for Reaction-Diffusion System ⋮ Group classification of systems of nonlinear reaction-diffusion equations with general diffusion matrix. II: Generalized Turing systems ⋮ Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses ⋮ Conditional symmetry of a system of nonlinear reaction-diffusion equations ⋮ Galilei's relativity principle for a system of reaction-convection-diffusion equations ⋮ Systems of reaction-convection-diffusion equations invariant under Galilean algebras ⋮ New classes of exact solutions to general nonlinear equations and systems of equations in mathematical physics ⋮ New classes of exact solutions to nonlinear systems of reaction-diffusion equations ⋮ Nonclassical symmetries of a system of nonlinear reaction-diffusion equations ⋮ Nonlocal symmetries of the system of chemotaxis equations with derivative nonlinearity

Cites Work

• Symmetry reductions and exact solutions of a class of nonlinear heat equations
• Galilei-invariant nonlinear systems of evolution equations
• Lie symmetries and multiple solutions in reaction-diffusion systems
• Higher symmetries and exact solutions of linear and nonlinear Schrödinger equation
• Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I
• Extended supersymmetries for the Schrödinger–Pauli equation
• The use of Lie transformation groups in the solution of the coupled diffusion equation

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