Diffusive Lotka-Volterra System: Lie Symmetries and Exact and Numerical Solutions
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.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 10, pp 1665-1675.
Citation Example: Cherniga R. M., Dushka V. A. Diffusive Lotka-Volterra System: Lie Symmetries and Exact and Numerical Solutions // Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1395-1404.