论文标题
界面毛细血管 - 重力孤立波的存在和稳定性持续涡度
Existence and stability of interfacial capillary-gravity solitary waves with constant vorticity
论文作者
论文摘要
在本文中，我们认为毛细血管 - 重力波在界面上传播，分隔了有限深度和恒定密度的两个流体。假定每一层中的流量是不可压缩的，并且具有恒定的涡度。我们通过空间动力学方法证明了该系统中该系统中对该系统的小振幅孤立波解的存在。然后，我们使用经典的grillakis--shatah--strauss（GSS）方法来研究这些波的轨道稳定性/不稳定。我们找到表征稳定性属性的参数（Froude号，键号以及深度和密度比）的明确函数。特别是，有条件的轨道稳定和不稳定的波是可能的。
In this paper, we consider capillary-gravity waves propagating on the interface separating two fluids of finite depth and constant density. The flow in each layer is assumed to be incompressible and of constant vorticity. We prove the existence of small-amplitude solitary wave solutions to this system in the strong surface tension regime via a spatial dynamics approach. We then use a variant of the classical Grillakis--Shatah--Strauss (GSS) method to study the orbital stability/instability of these waves. We find an explicit function of the parameters (Froude number, Bond number, and the depth and density ratios) that characterizes the stability properties. In particular, conditionally orbitally stable and unstable waves are shown to be possible.
