Exact Solutions and Optimal System of Hyperbolic Monge-Ampère Equation

Abstract

Based on Lie symmetry theory, the exact solutions of the hyperbolic Monge-Ampère equation are studied. Firstly, the invariance of the Lie symmetry group is applied to obtain the six-dimensional Lie algebras, then the commutator table and the adjoint representation of the equation are obtained, based on which the optimal system is found. Finally, the exact solutions are obtained by symmetry reduction which transforms the PDEs into easily solvable ODEs.