Lie-B "acklund symmetry and non-invariant solutions of nonlinear\n evolution equations

2017/01/13 by Ivan Tsyfra, Tsyfra, Ivan M., Wojciech Rzeszut +3
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.1701.03722

Abstract

We study the symmetry reduction of nonlinear partial differential equations\nwhich are used for describing diffusion processes in nonhomogeneous medium. We\nfind ansatzes reducing partial differential equations to systems of ordinary\ndifferential equations. The ansatzes are constructed by using operators of\nLie-B "acklund symmetry of third order ordinary differential equation. The\nmethod gives the possibility to find solutions which cannot be obtained by\nvirtue of classical Lie method. Such solutions have been constructed for\nnonlinear diffusion equations which are invariant with respect to\none-parameter, two-parameter and three-parameter Lie groups of point\ntransformations.\n

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