标题： 浅水流在渐变斜坡和底部摩擦下的孤立波和波动激波的演变 显示英文标题

标题： Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction

摘要： 本文考虑在变系数Korteweg-de Vries方程框架下，渐变斜坡和底部摩擦作用下浅水孤立波和非线性周期波的传播。 我们使用Whitham平均方法，利用该理论在受扰可积方程中的最新发展。 这种一般方法不仅使我们能够改进已知结果，即在变地形和底部摩擦（由Chezy定律建模）存在的情况下孤立孤波和周期波列的绝热演化，而且重要的是，可以研究这些因素对波动激波传播的影响，波动激波在所考虑的系统中本质上是不稳定的。 特别是，结果表明，变地形和底部摩擦的共同作用通常会对波动激波的传播施加一定的全局限制，使得领先孤波的演化与具有相同初始振幅的孤立孤波的演化有显著不同。 这种非局部效应是由于波动激波内部的非线性波相互作用引起的，可能导致额外的孤波振幅增长，这在传统绝热方法框架下无法预测孤波在缓慢变化介质中的传播。 显示英文摘要

摘要： This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging method, using a recent development of this theory for perturbed integrable equations. This general approach enables us not only to improve known results on the adiabatic evolution of isolated solitary waves and periodic wave trains in the presence of variable topography and bottom friction, modeled by the Chezy law, but also importantly, to study the effects of these factors on the propagation of undular bores, which are essentially unsteady in the system under consideration. In particular, it is shown that the combined action of variable topography and bottom friction generally imposes certain global restrictions on the undular bore propagation so that the evolution of the leading solitary wave can be substantially different from that of an isolated solitary wave with the same initial amplitude. This non-local effect is due to nonlinear wave interactions within the undular bore and can lead to an additional solitary wave amplitude growth, which cannot be predicted in the framework of the traditional adiabatic approach to the propagation of solitary waves in slowly varying media.