物理学报Issue(20)：1-9,9.DOI:10.7498/aps.63.200203
变系数Whitham-Bro er-Kaup方程组的对称、约化及精确解
Exact solutions of Whitham-Bro er-Kaup equations with variable co efficients
摘要
Abstract
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.关键词
变系数Whitham-Broer-Kau方程组/修正的Clarkson-Kruskal直接法/相似约化/精确解Key words
Whitham-Broer-Kaup equations with variable coefficients/modified Clarkson-Kruska direct method/similarity reductions/exact solutions引用本文复制引用
刘勇,刘希强..变系数Whitham-Bro er-Kaup方程组的对称、约化及精确解[J].物理学报,2014,(20):1-9,9.基金项目
国家自然科学基金委员会-中国工程物理研究院联合基金(批准号:11076015)资助的课题.* Project supported by the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant No.11076015) （批准号:11076015）
