Whitham-Broer-Kaup浅水波方程的对称性约化

SYMMETRY REDUCTIONS OF WHITHAM-BROER-KAUP EQUATIONS IN SHALLOW WATER

本文利用群论方法和直接法给出Whitham-Broer-Kaup浅水波方程的5种类型的对称性约化。群论方法得到的Painlev Ⅱ型约化仅仅是直接法约化的一种特殊情况。在直接法的约化结果中包含有关于时间变量t的3种类型的奇点:极点,代数支点和对数支点。

In this paper, five types of similarity reductions of Whitham-Broer-kaup equations in shallow water are given by both the classical Lie approach and the direct method. The Painleve 11 type reduction equation obtained by the classical Lie approach is only the special case of that obtained by the direct method. In the similarity reduction results of the direct method, three types of singularity points, i.e., poles, algebraic branch points and logarithmic branch points. are included.