Group Analysis of Differential Equations and Integrable Systems − 2018
(AGH University of Science and Technology, Krakow, Poland)
On a generalized symmetry method of reduction of nonlinear evolution and
wave type equations
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.