Mathematical Sciences: Numerical Studies of Nonlinear Waves

这一建议是关于在流体表面传播的波的研究。一个重要的例子是在水面上以恒定速度移动的障碍物（如船只）所产生的一系列波浪。现有的理论是基于一些简化的假设。建议通过消除其中一些假设来扩展和改进现有理论。预计这项研究将发现新的解决方案家族。特别提出了研究一层泥浆对船舶波浪的影响。提出的方法是用润滑理论推导出的合适的边界条件来代替经典的刚性底部假设。还提出了计算存在涡度和表面张力的周期波和孤立波的方法。先前和初步的计算表明，有许多不同的解族。本文拟对它们进行进一步的研究，并对孤立波之间的相互作用进行数值计算。

DMS-9500956 Vanden-Broeck This proposal is concerned with the study of waves propagating at the surface of a fluid. An important example is the train of waves generated by an obstacle (i.e. a ship) moving at a constant velocity at the surface of water. Existing theories are based on a number of simplifying assumptions. It is proposed to extend and improve existing theories by removing some of these assumptions. It is expected that the research will uncover new families of solutions. In particular it is proposed to study the effect of a layer of mud on ship waves. The proposed approach consists of replacing the classical assumption of a rigid bottom by an appropriate boundary condition derived from lubrication theory. It is also proposed to calculate periodic and solitary waves in presence of vorticity and surface tension. Previous and preliminary calculations have shown that there are many different families of solutions. It is intended to study them further and to calculate numerically the interaction between solitary waves.