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含色散项Zabolotskaya-Khokhlov方程的对称、约化、精确解和守恒律

Symmetries, reductions, exact solutions and conservation laws of Zabolotskaya-Khokhlov equation with dissipative term

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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。

Abstract

Using the modified Clarkson-Kruskal direct method, the symmetries reductions of the Zabolotskaya-Khokhlov equation with a dissipative term were obtained. By solving the reduction equations, a great many of solutions were derived, including the rational function solutions, the trigonometric function solutions, hyperbolic function solutions and so on. The conservation laws were given at last.

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中图分类号:O175.29

DOI:10.3969/j.issn.1007-5461. 2015.01.007

所属栏目:量子物理

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

收稿日期:2014-04-28

修改稿日期:2014-06-25

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作者单位    点击查看

冯春明:聊城大学东昌学院, 山东 聊城 252059
刘庆松:聊城大学学报编辑部, 山东 聊城 252059

联系人作者:冯春明(84666480@qq.com)

备注:冯春明 (1974-), 山东人,讲师,硕士,从事非线性发展方程研究和教学。

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引用该论文

FENG Chunming,LIU Qingsong. Symmetries, reductions, exact solutions and conservation laws of Zabolotskaya-Khokhlov equation with dissipative term[J]. Chinese Journal of Quantum Electronics, 2015, 32(1): 46-52

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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