Monday, August 5, 2013

1105.5303 (Stephen C. Anco et al.)

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

Stephen C. Anco, Sajid Ali, Thomas Wolf
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.
View original:

No comments:

Post a Comment