| 含色散项Zabolotskaya-Khokhlov方程的对称、约化、精确解和守恒律 |
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| 引用本文： | 冯春明,刘庆松.含色散项Zabolotskaya-Khokhlov方程的对称、约化、精确解和守恒律[J].量子电子学报,2015,32(1):46-52. |
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| 作者姓名： | 冯春明 刘庆松 |
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| 作者单位： | 1.聊城大学东昌学院，山东 聊城 252059;2.聊城大学学报编辑部，山东 聊城 252059 |
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| 基金项目： | 国家自然科学基金;中国工程物理研究院联合基金(11076015);聊城大学东昌学院课题(2013LG001)资助 |
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| 摘 要： | 利用修正的Clarkson-Kruskal(CK)直接方法得到了含色散项的Zabolotskaya-Khokhlov(简写为DZK)方程的对称、约化和一些精确解,包括双曲函数解,有理函数解,三角函数解等,同时得到了该方程的守恒律.
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| 关 键 词： | 非线性方程 修正的Clarkson-Kruskal直接方法 DZK方程 对称、约化 精确解 守恒律 |
| 收稿时间： | 2014-04-28 |
| 修稿时间： | 2014-11-07 |
Symmetries,reductions, exact solutions and conservation laws of the Zabolotskaya-KhokhlovEquation with a Dissipative Term |
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| FENG Chun-ming,LIU Qing-song.Symmetries,reductions, exact solutions and conservation laws of the Zabolotskaya-KhokhlovEquation with a Dissipative Term[J].Chinese Journal of Quantum Electronics,2015,32(1):46-52. |
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| Authors: | FENG Chun-ming LIU Qing-song |
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| Affiliation: | 1.School of Dongchang, Liaocheng University, Liaocheng 252059,China;2. Editoral Department, Journal of Liaocheng University, Liaocheng 252059, China |
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| Abstract: | Using the modified Clarkson–Kruskal direct method, the symmetries reductions of the Zabolotskaya-KhokhlovEquation with a Dissipative Term are obtained. By solving the reduction equations, a great many of solutions are derived, including the rational functions solution, the trigonometric functions, hyperbolic functions and so on. The conservation laws are given at last. |
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| Keywords: | the modified CK’s direct method the DZK equation symmetry reduction exact solutions conservation laws |
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