标题： 非均匀介质中的非对称弯曲重力孤立波 显示英文标题

标题： Asymmetric Flexural-gravity Lumps in Nonuniform Media

摘要： 在这里，我们展示了在粘性为零且无旋的流体表面覆盖有变化厚度弹性材料的情况下，只要厚度仅在一个方向上变化并且有一个局部最小值，非对称的完全局域化的弯曲重力块状波可以传播。我们推导并给出了允许弯曲材料在传播方向的横向有小变化的弯曲重力波包包络演化方程。我们表明，控制方程属于Davey-Stewartson方程的一般族，但表面演化方程中多了一个额外项，用于考虑弹性覆盖层的可变厚度。然后，我们使用迭代牛顿-拉夫森方案，并通过拉格朗日插值进行数值延续过程，以寻找该方程组的完全局域化解。我们表明，如果弹性片厚度至少有一个局部最小值，弯曲重力块状波可以在最小厚度附近传播，并且通常在传播方向的横向具有非对称的钟形。在应用物理中，弯曲重力波描述了例如冰盖下水体上的波传播。冰层很少是均匀的，海底也是如此，实际上在边界（冰缘、海岸线）附近它们通常仅在一个方向上变化（朝向边缘），并在横向方向上是均匀的。这项研究表明，完全局域化的波不仅限于恒定冰厚/水深区域，而可以在更广泛的条件下存在。所呈现的结果可能对弯曲重力（以及毛细重力）块状波的实验生成和观测具有重要意义。 显示英文摘要

摘要： Here we show that asymmetric fully-localized flexural-gravity lumps can propagate on the surface of an inviscid and irrotational fluid covered by a variable-thickness elastic material, provided that the thickness varies only in one direction and has a local minimum. We derive and present equations governing the evolution of the envelope of flexural-gravity wave packets allowing the flexing material to have small variations in the transverse (to propagation) direction. We show that the governing equation belongs to the general family of Davey-Stewartson equations, but with an extra term in the surface evolution equation that accounts for the variable thickness of the elastic cover. We then use an iterative Newton-Raphson scheme, with a numerical continuation procedure via Lagrange interpolation, in a search to find fully-localized solutions of this system of equations. We show that if the elastic sheet thickness has (at least) a local minimum, flexural-gravity lumps can propagate near the minimum thickness, and in general have an asymmetric bell-shape in the transverse to the propagation direction. In applied physics, flexural-gravity waves describe for instance propagation of waves over the ice-covered bodies of water. Ice is seldom uniform, nor is the seafloor, and in fact near the boundaries (ice-edges, shorelines) they typically vary only in one direction (toward to edge), and are uniform in the transverse direction. This research suggests that fully localized waves are not restricted to constant ice-thickness/water-depth areas and can exist under much broader conditions. Presented results may have implications in experimental generation and observation of flexural-gravity (as well as capillary-gravity) lumps.