TY - JOUR
T1 - Exact Solutions and Optimal System of Hyperbolic Monge-Ampère Equation
AU - Xu , Hui
AU - Liu , Minyuan
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 919
EP - 929
PY - 2024
DA - 2024/12
SN - 6
DO - http://doi.org/10.12150/jnma.2024.919
UR - https://global-sci.org/intro/article_detail/jnma/23663.html
KW - Optimal system, exact solution, Lie symmetry, hyperbolic Monge-Ampère equation.
AB - <p style="text-align: justify;">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.</p>