Lie-Backlund symmetry, reduction and solutions of nonlinear evolution equations - Rzeszut, W.; Tsyfra, I. M.; Vladimirov, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.9 We study the symmetry reduction of nonlinear partial differential equations which are used for describing diffusion processes in a nonhomogeneous medium. We find ansatzes reducing partial differential equations to systems of ordinary differential equations. The ansatzes are constructed by using operators of Lie–Backlund symmetry of the third order ordinary differential equation. The method gives a possibility to find solutions which can not be obtained by virtue of the classical Lie method. Such solutions were constructed for nonlinear diffusion equations which are invariant with respect to one-parameter, two-parameter, and three-parameter Lie groups of point transformations.