Geodesic
On multidimensional exact solutions of a nonlinear reaction--diffusion system
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 2, pp. 225-239

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We study a multidimensional case of a nonlinear reaction-diffusion system modeled by a system of two parabolic equations with power nonlinearities. Such systems can be used to simulate the process of propagation in space of interacting distributed formations of robots of two types. Such equations also describe the processes of nonlinear diffusion in reacting two-component continuous media. An original version of the reduction method is proposed, which reduces the construction of the dependence of the exact solution on spatial variables to the solution of the Helmholtz equation, and the dependence on time to the solution of a linear system of ordinary differential equations. A number of examples of multiparameter families of exact solutions given by elementary functions are constructed.
Mots-clés : reaction–diffusion system, exact solutions.
Keywords: reduction 
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     title = {On multidimensional exact solutions of a nonlinear reaction--diffusion system},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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A. A. Kosov; È. I. Semenov; V. V. Tirskikh. On multidimensional exact solutions of a nonlinear reaction--diffusion system. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 2, pp. 225-239. http://geodesic.mathdoc.fr/item/VUU_2023_33_2_a2/