Group Analysis of Differential Equations and Integrable Systems − 2018


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

On a generalized symmetry method of reduction of nonlinear evolution and wave type equations

Abstract:
We study the symmetry reduction of partial differential equations with two independent variables. We construct the ansatz for dependent variable or its derivatives which reduces the scalar partial differential equation to a system of ordinary differential equations. One can obtain the ansatz for dependent variable by solving ordinary differential equation admitting the operators of generalized symmetry. We show that the method can be applied to nonevolution equations. The method gives the possibility to find solutions which cannot be obtained by virtue of classical Lie method.