Ivan Tsyfra (AGH University of Science and Technology, Kraków, Poland)
Wojciech Rzeszut (Jagiellonian University, Kraków, Poland)
Vsevolod Vladimirov (AGH University of Science and Technology, Kraków, Poland)

Lie–Bäcklund symmetry and construction of noninvariant solutions to nonlinear evolution equations

Abstract:
We use operators of Lie–Bäcklund symmetry of ordinary differential equations to construct ansatzes reducing partial differential equations to a system of ordinary differential equations. We study the conditions when this approach enables us to obtain solutions which are not invariant ones in the classical Lie sense.