By means of a conformal mapping and bifurcation theory, we prove the existence of large-amplitude steady stratified periodic water waves, with a density function depending linearly on the streamfunction, which may have critical layers and overhanging profiles. We also provide certain conditions for which these waves cannot overturn.

中文翻译：

---

具有临界层的分层大振幅稳态周期性水波

通过共形映射和分岔理论，我们证明了大振幅稳定分层周期性水波的存在，其密度函数线性依赖于流函数，可能具有临界层和悬垂剖面。我们还提供了这些波浪不能翻转的某些条件。