论文标题
深水内部毛细血管钻波的渐近模型
An asymptotic model for internal capillary-gravity waves in deep water
论文作者
论文摘要
本文考虑的是一个双向模型，用于在两层流体系统中传播界面毛细血管 - 重力波，该系统具有刚性盖子条件的上层和下层，其深度更大或无限。该系统源自界面的内部波的重新印度，在界面中具有不可忽略的表面张力效应，而本杰明·诺诺（Benjamin-Ono）方向下的相应渐近模型则得出。还引入了另一个单向模型，即所谓的正则本杰明方程，概括了本杰明蛋白方程。讨论了新方程的适应性和孤立波解的存在。
Considered in this paper is a bi-directional model for the propagation of interfacial capillary-gravity waves in a two-layer system of fluids with rigid lid condition for the upper layer and lower layer with a much larger or infinite depth. The system is derived from a reformulation of the Euler equations for internal waves with nonnegligible surface tension effects in the interface and the corresponding asymptotic model under the Benjamin-Ono regime. Another unidirectional model, so-called regularized Benjamin equation, generalizing the Benjamin equation, is also introduced. Well-posedness of the new equations and existence of solitary wave solutions are discussed.
