The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for the fluid flow, in the form of a nearly-integrable non-autonomous Hamiltonian with aperiodic time dependence. The proofs use the tools of perturbation theory in the real-analytic setting. The obtained Hamiltonian provides a natural example in the context of the aperiodically time-dependent Hamiltonian systems studied in Fortunati and Wiggins (2016). Some key properties of the system at hand, such as the stability, can be addressed as a consequence of this theory.

中文翻译：

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任意测深上的行波：局部稳定性结果

在浅水公式中研究了半无限通道中任意准平坦测深上的行波问题。它显示了如何在流体流动的椭圆平衡附近以具有非周期时间依赖性的几乎可积分的非自治哈密顿量的形式来投射流函数。证明在实分析环境中使用了微扰理论的工具。在 Fortunati 和 Wiggins (2016) 研究的非周期性时间相关哈密顿系统的背景下，获得的哈密顿量提供了一个自然的例子。手头系统的一些关键属性，例如稳定性，可以作为该理论的结果来解决。