TY - JOUR
A1 - Anco, Stephen
A1 - Ali, Sajid
A1 - Wolf, Thomas
T1 - Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
T2 - SIGMA 7
N2 - 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.
Y1 - 2011
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/4628
ER -