Diffusive Lotka-Volterra System: Lie Symmetries and Exact and Numerical Solutions

Abstract

We present a complete description of Lie symmetries for the nonlinear diffusive Lotka-Volterra system. The results are used for the construction of exact solutions of the Lotka-Volterra system, which, in turn, are used for solving the corresponding nonlinear boundary-value problems with zero Neumann conditions. The analytic results are compared with the results of computation based on the finite-element method. We conclude that the obtained exact solutions play an important role in solving Neumann boundary-value problems for the Lotka-Volterra system.