Abstract

The problem of the propagation of waves of small amplitude on the surface of shallow water in a reservoir of variable depth is considered. The Korteweg-de Vries (KdV) equation with a variable coefficient taking into account both the bottom profile and the geometric divergence of waves is obtained from the system of shallow water equations. The inverse problem, which consists of determining the variable bottom profile by the period and amplitude of stationary waves, is posed and solved within the adiabatic approximation. It is shown that taking into account the geometric divergence of the waves significantly affects the solution of the inverse problem.

中文翻译：

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变深水池中浅水方程的一个反问题的求解

摘要

考虑了小振幅波在变深水库中浅水表面的传播问题。具有可变系数的 Korteweg-de Vries (KdV) 方程同时考虑了底部剖面和波浪的几何发散度，是从浅水方程系统中获得的。逆问题包括通过驻波的周期和振幅确定可变底部剖面，在绝热近似内提出并解决。结果表明，考虑波的几何发散会显着影响逆问题的求解。