Lie Symmetry Analysis and Exact Solutions of Tzitzeica Surfaces PDE in Galilean Space

Abstract

In this paper, we give the problem how to construct the Tzitzeica surfaces PDE, which is a special MongeAmpere equation, from a Tzitzeica surface in Galilean space. We examine these PDE equation from the point of the Lie symmetry analysis. Then, the new classes of symmetry reductions of the Tzitzeica surfaces PDE are designated and exact solutions are investigated. Also we illustrate a Tzitzeica surface for one of our cases.