  We construct large families of two-dimensional travelling water waves
propagating under the influence of gravity in a flow of constant vorticity over
a flat bed. A Riemann-Hilbert problem approach is used to recast the governing
equations as a one-dimensional elliptic pseudo-differential 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.

Analysis of PDEs