Exact and numerical solutions of the generalized fisher equation

Multiparameter families of exact solutions to the generalized Fisher equation (which is a simplification of the known coupled reaction-diffusion system describing spatial segregation of interacting species) have been found using the classical Lie approach and the method of additional generating conditions. The exact solutions are applied next to solving a nonlinear boundary-value problem with the zero Neumann conditions. Analytical results are compared with numerical calculations by using the finite elements method. It is concluded that the obtained exact solutions play an important role for the generalized Fisher equation.