Reducing of system of partial differential equations and generalized symmetry of ordinary differential equations

Abstract: Symmetry reductions of systems of two nonlinear partial differential equations are studied. We find ansatzes reducing system of partial differential equations to system of ordinary differential equations. The method is applied to system related to Korteweg -- de Vries (KdV) equation, and reaction-diffusion equations. We have also shown the possibility of constructing solution to system of non-evolutionary equations, which contains one or two arbitrary functions.