TY - GEN A1 - Anco, Stephen A1 - Ali, Sajid A1 - Wolf, Thomas T1 - Exact solutions of nonlinear partial differential equations by the method of group foliation reduction 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 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. T3 - ZIB-Report - 11-25 KW - semilinear heat equation, similarity reduction, exact solutions, group foliation, symmetry Y1 - 2011 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1317 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-13171 ER -