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.
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Cherniha, R.M. New Exact Solutions of One Nonlinear Equation in Mathematical Biology and Their Properties. Ukrainian Mathematical Journal 53, 1712–1727 (2001). https://doi.org/10.1023/A:1015252112419
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DOI: https://doi.org/10.1023/A:1015252112419