Publication: Exact solutions of nonlinear partial differential equations by the method of group-foliation reduction

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Title	Exact solutions of nonlinear partial differential equations by the method of group-foliation reduction
Authors/Editors*	S C Anco, S Ali, T Wolf
Where published*	SIGMA
How published*	Journal
Year*	2011
Volume	7
Number	066
Pages	10
Publisher
Keywords	semilinear heat equation, similarity reduction, exact solutions, group foliation, symmetry
Link	http://www.emis.de/journals/SIGMA/2011/066/
Abstract	A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method is based on group foliation reduction and employs a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation.