Lie-Backlund symmetry reduction of nonlinear and non-evolution equations

Abstract

The application of Lie-Backlund symmetry operators admitted by ordinary differential equations for reducing partial differential equations are studied. The ansatze for dependent variable are constructed by integrating ordinary differential equations. We show that the method is applicable for nonlinear evolution and non-evolution types equations. In the framework of the approach we construct the solution depending on arbitrary smooth function on one variable