Symmetries and Integrability Properties of Generalized Fisher Type Nonlinear Diffusion Equation

Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized Fisher type equation to obtain physically interesting solutions using Lie symmetry analysis. In particular, we report several travelling wave patterns, static patterns and localized structures depending upon the choice of the parameters involved.