Optimal system and conservation laws for the generalized Fisher equation in cylindrical coordinates

Abstract

The reaction diffusion equation arises in physical situations in problems from population growth, genetics and physical sciences. In many practical situations, the physical domain of the problem is adequately described in cylindrical Coordinates. Therefore, we consider the Fisher equation in cylindrical coordinates. We consider the generalised Fisher equation in cylindrical coordinates from Lie theory stand point. An invariance method is performed and the optimal set of nonequivalent symmetries is obtained. Finally, the  conservation laws are constructed using ’multiplier method’. We determine multipliers as functions of the dependent and independent variables only. The conservation laws are computed and presented in terms of conserved vector corresponding to each multiplier.