We prove the existence of small amplitude time quasi-periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a Nash-Moser implicit function iterative scheme we construct traveling nonlinear waves which pass through each other slightly deforming and retaining forever a quasiperiodic structure. These solutions exist for any fixed value of depth and gravity and restricting the vorticity parameter to a Borel set of asymptotically full Lebesgue measure.

中文翻译：

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具有恒定涡度的纯重力行进准周期水波

我们证明了对于由空间周期自由界面界定的平底上的二维流体，具有恒定涡度的纯重力水波方程的小振幅时间准周期解的存在。使用 Nash-Moser 隐式函数迭代方案，我们构造了行进的非线性波，这些行波彼此轻微变形并永远保留准周期结构。这些解对于深度和重力的任何固定值都存在，并将涡度参数限制为渐近完整勒贝格测度的 Borel 集。