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| Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Amp`ere Equation |
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Citation： |
Zhongzhou DONG,Yong CHEN,Dexing KONG,Zenggui WANG.Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Amp`ere Equation[J].Chinese Annals of Mathematics B,2012,33(2):309~316 |
| Page view： 2084
Net amount： 1773 |
Authors： |
Zhongzhou DONG; Yong CHEN; Dexing KONG; Zenggui WANG; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10735030, 90718041, 11075055), the Shanghai Leading Academic Discipline Project (No. B412), the Innovative Research Team Program of the National Natural Science Foundation of China (No. 61021004), the Tianyuan Fund for Mathematics (No. 11126120)
and the Doctor Foundation of Henan Polytechnic University (No. B2011-006). |
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| Abstract： |
By means of the classical symmetry method, a hyperbolic Monge-Amp\`{e}re 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-Amp\`{e}re equation, from which two interesting classes of solutions to the hyperbolic Monge-Amp\`{e}re equation are obtained successfully. |
Keywords： |
Symmetry reduction, Monge-Amp\`{e}re equation, Exact solutions |
Classification： |
22E50, 22E60, 35L70 |
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