Solving Model of Reaction-Diffusion System in Ecological by Symmetry Lie Group Methods

Abstract

In this paper, we will use analytical methods for solving the fundamental element of a reaction diffusion model in ecology. The model denotes an interaction between two species which describe ecological predations, and mathematically is defined as a system of partial differential equations with initial and boundary conditions. Symmetry Lie group methods are used to transform this model into a system of ordinary differential equations, then this system solved by generalized tanh function method when there exists a small parameter    appear in one of the equation.