Traveling waves in interfacial fluid dynamics with multi-valued height

The traditional approach to traveling waves in interfacial fluid dynamics assumes that the free surface is a graph with respect to the horizontal coordinate.  In the
presence of effects such as surface tension, however, there are known to exist traveling waves with multivalued height.  We give a new formulation of the
traveling wave problem utilizing a paramterized curve, so that there is no difference between a single-valued or a multivalued interface.  We will present a global
bifurcation theorem using this formulation, and present associated numerical results. This includes joint work with Benjamin Akers, Kevin Pond, Walter Strauss, and J. Douglas Wright.