Lie-Backlund symmetry, reduction and solutions of nonlinear evolution equations

  • W. Rzeszut AGH University of Science and Technology, Krakow, Poland
  • I. M. Tsyfra AGH University of Science and Technology, Krakow, Poland; The Institute of Geophysics of the National Academy of Sciences of Ukraine
  • V. A. Vladimirov AGH University of Science and Technology, Krakow, Poland
Keywords: Lie-Backlund symmetry operators, ordinary differential equations, partial differential equations, reduction, invariant solutions


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.


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How to Cite
Rzeszut, W., I. M. Tsyfra, and V. A. Vladimirov. “Lie-Backlund Symmetry, Reduction and Solutions of Nonlinear Evolution Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 3, Apr. 2022, pp. 342-50, doi:10.37863/umzh.v74i3.7007.
Research articles