Stability and dynamics of solitary gravity-capillary waves

当重力和表面张力的影响在大小上相似时，重力-毛细管波是水表面上的波。这些波的波长大约为1-2厘米。例如，正是在这种长度尺度上，风浪的产生才开始发生，而用来研究海洋表面和探测漏油的某些形式的遥感雷达可以探测到这些海浪。我们将在非线性区域研究这些波，其中孤立波在动力学中起着重要的作用。我们将使用完整的流体力学方程，并推导和验证更简单的模型方程，因为在复杂的流动中，完整的方程在计算上很难求解。

Gravity-capillary waves are waves on the water's surface when the effects of both gravity and surface tension are similar in magnitude. These waves have a wavelength of approximately 1-2 cm. It is at this length scale, for example, that the initiation of the generation of wind ripples occurs and it is these waves that can be detected by some forms of remote sensing radars used to study the surface of the ocean and for detecting oil spills. We shall study these waves in the nonlinear regime, where solitary waves play an important role in the dynamics. We will use both the full equations of fluid dynamics and also derive and validate model equations that are simpler given that in complex flows, the full equations are computationally diffucult to solve.