Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
- 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.
| Author: | Stephen Anco, Sajid Ali, Thomas Wolf |
|---|---|
| Document Type: | Article |
| Parent Title (English): | SIGMA 7 |
| Year of first publication: | 2011 |
| Preprint: | urn:nbn:de:0297-zib-13171 |
| DOI: | https://doi.org/10.3842/SIGMA.2011.066 |
