变系数Whitham-Broer-Kaup方程组的对称、约化及精确解

Exact solutions of Whitham-Broer-Kaup equations with variable coefficients

利用修正的Clarkson-Kruskal直接法对变系数Whitham-Broer-Kaup(VCWBK)方程组进行等价转化,建立了VCWBK方程组与常系数WBK方程组解之间的关系,并得到了常系数WBK方程组的一些对称和相似约化.借助辅助函数法得到了VCWBK方程组的一些新精确解,包括有理函数解、双曲函数的解、三角函数解和Jacobi椭圆函数解.

An equivalence transformation of Whitham-Broer-Kaup equations with variable coefficients （VCWBK） is obtained by using modified Clarkson-Kruskal direct method. Further, the relationship between the solutions of VCWBK equations and ones of the corresponding WBK equations with constant coefficients is obtained. In addition, by applying direct symmetry method, some symmetries and similarity reductions of the corresponding WBK equations with constant coefficients are derived. Using an auxiliary function to solve some special cases, we obtain some new exact solutions of VCWBK equations, including rational solutions, hyperbolic function solutions, trigonometric function solutions, and Jacobi elliptic function solutions.