On a reduction of nonlinear partial differential equations via non-point symmetry method

Abstract:
We study the symmetry reduction of nonlinear partial differential equations by using operators of non-point symmetry. We construct the ansatz for dependent variable or its derivatives which reduces differential equation under study to a system of ordinary differential equations. By using operators of Lie−Backlund symmetry we construct the solutions of no nonlinear hyperbolic equations and Plebanski's heavenly equation depending on smooth functions of one variable.