任意水深上的行波：扰动理论方法
Travelling waves over an arbitrary bathymetry: a perturbation theory approach
摘要：
本文用浅水方程研究了半无限深槽中任意准平水深上的行波问题。它示出了如何流函数可以铸造，在附近的椭圆平衡的流体流动，在一个几乎可积的非自治的哈密顿量的形式与非周期性的时间依赖性。证明使用的工具，扰动理论在真正的分析设置。所获得的哈密顿量在Escherati和Wiggins（2016）研究的非周期性时间依赖哈密顿系统的背景下提供了一个自然的例子。系统的一些关键特性，如稳定性，可以作为这个理论的结果来解决。
英文摘要：
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.
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