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Volume 6, Issue 4
Exact Solutions and Optimal System of Hyperbolic Monge-Ampère Equation

Hui Xu & Minyuan Liu

DOI: 10.12150/jnma.2024.919

J. Nonl. Mod. Anal., 6 (2024), pp. 919-929.

Published online: 2024-12

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Optimal system, exact solution, Lie symmetry, hyperbolic Monge-Ampère equation.

  • AMS Subject Headings

35L70, 35A09, 35B06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-6-919, author = {Xu , Hui and Liu , Minyuan}, title = {Exact Solutions and Optimal System of Hyperbolic Monge-Ampère Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {4}, pages = {919--929}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.919}, url = {http://global-sci.org/intro/article_detail/jnma/23663.html} }
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 -

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.

Xu , Hui and Liu , Minyuan. (2024). Exact Solutions and Optimal System of Hyperbolic Monge-Ampère Equation. Journal of Nonlinear Modeling and Analysis. 6 (4). 919-929. doi:10.12150/jnma.2024.919
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