Optimal System and Exact Solutions of Monge-Ampere Equation

Abstract

A solution that remains unchanged when transformed under Lie group of point symmetries of the differential equation is an invariant solution of the differential equation. Optimal system of Lie group of point symmetry generators provide all possible invariant solutions of differential equation. Here, using optimal system of Lie point symmetry generators group invariant solutions are obtained. Using these solutions, exact solutions of non-homogeneous Monge-Ampere equation have been presented here.