We study the problem of symmetry reduction of nonlinear partial differential equations used to describe diffusion processes in an inhomogeneous medium. We find ansatzes reducing partial differential equations to systems of ordinary differential equations. These ansatzes are constructed by using the operators of Lie–Bäcklund symmetry of the third-order ordinary differential equations. The proposed method enables us to find solutions that cannot be obtained by using the classical Lie method. These solutions are constructed for nonlinear diffusion equations invariant under one-, two-, and three-parameter Lie groups of point transformations.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 3, pp. 342–350, March, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i3.7007.
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Rzeszut, W., Tsyfra, I.M. & Vladimirov, V.A. Lie–Bäcklund Symmetry, Reduction, and Solutions of Nonlinear Evolutionary Equations. Ukr Math J 74, 385–394 (2022). https://doi.org/10.1007/s11253-022-02070-w
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DOI: https://doi.org/10.1007/s11253-022-02070-w