2019
Том 71
№ 11

All Issues

New Exact Solutions of One Nonlinear Equation in Mathematical Biology and Their Properties

Cherniga R. M.

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Abstract

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.

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