论文标题
带有可变的测深和电流的浅水上的无反射波传播。 ii
Reflectionless wave propagation on shallow water with variable bathymetry and current. II
论文作者
论文摘要
我们表明，在线性近似中，在通道中的浅水表面上有三类无反射波传播，其深度，宽度和电流速度在空间上有变化。这些类别中有两个在我们的之前的论文（Churilov＆Stepanyants，2022）中进行了描述，最近发现了第三个类，并在此处进行了描述。对问题的一般分析表明，在我们的两篇论文中使用的方法中，这三个类别显然耗尽了所有可能的问题解决方案的可能情况。我们表明，在某些条件下，无反射流可以是全局的，即它可以存在于整个X轴上。也有无反射流，仅在X轴的有限间隔内存在。
We show that in the linear approximation there are three classes of reflectionless wave propagation on a surface of shallow water in the channel with spatially varying depth, width, and current speed. Two of these classes have been described in our previous paper (Churilov & Stepanyants, 2022), and the third one was discovered recently and is described here. The general analysis of the problem shows that within the approach used in both our papers, these three classes, apparently, exhaust all possible cases of exact solutions of the problem considered. We show that the reflectionless flow can be global at certain conditions, i.e. it can exist on the entire x-axis. There are also reflectionless flows which exist only on the limited intervals of the x-axis.
