Geodesic
Analysis of reaction-diffusion systems by the method of linear determining equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 256-268

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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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     author = {A. V. Shmidt},
     title = {Analysis of reaction-diffusion systems by the method of linear determining equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {256--268},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a8/}
}
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A. V. Shmidt. Analysis of reaction-diffusion systems by the method of linear determining equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 256-268. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a8/