Exact Solutions and Optimal System of Hyperbolic Monge-Ampère Equation (Journal of Nonlinear Modeling and Analysis, 2024)
Based on Lie symmetry theory, the exact solutions of the hyperbolic Monge-Ampère equation are studied. Firstly, the invariance of the Liesymmetry group is applied to obtain the six-dimensional Lie algebras, then thecommutator table and the adjoint representation of the equation are obtained,based on which the optimal system is found. Finally, the exact solutions areobtained by symmetry reduction which transforms the PDEs into easily solvable ODEs.