中度振幅浅水波模型的行波解
Traveling wave solutions of a moderate amplitude shallow water wave model

作者利用平面动力系统定性分析方法研究一个描述中度振幅单向传播的浅水波模型的行波解. 根据可积系统的动力学性质, 作者讨论了该模型行波系统的分岔, 进而得到了光滑孤立波解, 周期波解, 周期尖波解, 紧孤立波解, 扭波解及反扭波解的存在条件, 并且给出了这些解的精确表达形式. 进一步利用数学软件Maple 18给出了这些有界行波解的数值模拟.
The author studies the traveling wave solutions of a shallow water wave model with moderate amplitude by qualitative analysis methods of planar dynamical systems. Using the dynamical properties of the integrable systems, we discuss the bifurcation of its traveling wave system, from which we obtain the existence conditions of the bounded traveling solutions, including solitary wave solutions, periodic wave solutions, kink-like wave solutions and antikink-like wave solutions, and the exact expressions of these traveling wave solutions. Furthermore, we simulate these solutions by the Maple 18 software to verify our results