We construct families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed, in particular establishing the existence of waves of large amplitude. A Riemann–Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudodifferential equation with a scalar constraint. The structural properties of this formulation, which arises as the Euler–Lagrange equation of an energy functional, enable us to develop a theory of analytic global bifurcation.

中文翻译：

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具有临界层的稳态重力水波的全局分岔

我们构建了二维行水波族，这些波在重力的影响下在平床上的恒定涡度流中传播，特别是确定了大振幅波的存在。黎曼-希尔伯特问题方法用于将控制方程重铸为具有标量约束的一维椭圆伪微分方程。这个公式的结构特性，作为能量泛函的欧拉-拉格朗日方程出现，使我们能够发展解析全局分叉的理论。