Ivan Tsyfra (AGH University of Science and Technology, Krakow, Poland)

Non-point symmetries and reduction of partial differential equations

Abstract:
We use operators of non-point symmetry to obtain ansatze for dependent variable and its derivatives which reduce partial differential equations to systems of ordinary differential equations. It turns out that the operators of conditional symmetry enables us to construct algorithmically the Backlund transformations to nonlinear wave equations. We construct exact solutions to nonlinear evolution and wave type equations by using this method.