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Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Amp`ere Equation |
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| Authors: | Zhongzhou DONG Yong CHEN Dexing KONG and Zenggui WANG |
| Institution: | 1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, Henan, China 2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China 3. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China 4. School of Mathematics Sciences, Liaocheng University, Liaocheng, 252059, Shandong, China |
| Abstract: | By means of the classical symmetry method, a hyperbolic Monge-Ampère equation is investigated. The symmetry group is studied and its corresponding group invariant solutions are constructed. Based on the associated vector of the obtained symmetry, the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation, from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully. |
| Keywords: | Symmetry reduction Monge-Ampère equation Exact solutions |
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