Exact steady periodic water waves with vorticity

We consider the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two-dimensional inviscid periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use bifurcation and degree theory to construct a global connected set of such solutions. (C) 2004 Wiley Periodicals, Inc.