New Exact Solutions of One Nonlinear Equation in Mathematical Biology and Their Properties
The classical Lie approach and the method of additional generating conditions are applied to constructing multiparameter families of exact solutions of the generalized Fisher equation, which is a simplification of the known coupled reaction–diffusion system describing spatial segregation of interacting species. The exact solutions are applied to solving nonlinear boundary-value problems with zero Neumann conditions. A comparison of the analytic results and the corresponding numerical calculations shows the importance of the exact solutions obtained for the solution of the generalized Fisher equation.
English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 10, pp 1712-1727.
Citation Example: Cherniga R. M. New Exact Solutions of One Nonlinear Equation in Mathematical Biology and Their Properties // Ukr. Mat. Zh. - 2001. - 53, № 10. - pp. 1409-1421.