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arXiv · 1105.5303

Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction

Stephen C. Anco·Sajid Ali·Thomas Wolf
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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 uses 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 group-foliation reduction 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.

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Stephen C. Anco, Sajid Ali, Thomas Wolf. 2013-08-02. Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction. https://doi.org/10.3842/sigma.2011.066

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