Abstract
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.
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Constantin, A., Strauss, W. & Vărvărucă, E. Global bifurcation of steady gravity water waves with critical layers. Acta Math 217, 195–262 (2016). https://doi.org/10.1007/s11511-017-0144-x
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DOI: https://doi.org/10.1007/s11511-017-0144-x