量子电子学报, 2015, 32 (1): 46, 网络出版: 2015-01-27
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
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 nonlinear equation modified Clark-Kruskal direct method DZK equation symmetry reduction exact solutions conservation laws
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.
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. 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.