Analysis of reaction-diffusion systems by the method of linear determining equations |
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Authors: | A V Schmidt |
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Institution: | (1) Institute of Computer Modeling, Siberian Division, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia |
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Abstract: | Exact solutions to two-component systems of reaction-diffusion equations are sought by the method of linear determining equations (LDEs) generalizing the methods of the classical group analysis of differential equations. LDEs are constructed for a system of two second-order evolutionary equations. The results of solving the LDEs are presented for two-component systems of reaction-diffusion equations with polynomial nonlinearities in the diffusion coefficients. Examples of constructing noninvariant solutions are presented for the reaction-diffusion systems that possess invariant manifolds. |
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Keywords: | system of reaction-diffusion equations method of linear determining equations method of exact solutions |
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