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

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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.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1395–1404, October, 2004.

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Cherniha, R.M., Dutka, V.A. Diffusive Lotka-Volterra System: Lie Symmetries and Exact and Numerical Solutions. Ukr Math J 56, 1665–1675 (2004). https://doi.org/10.1007/s11253-005-0142-6

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  • DOI: https://doi.org/10.1007/s11253-005-0142-6

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