Traveling Two and Three Dimensional Capillary Gravity Water Waves

Abstract

The main results of this paper are existence theorems for traveling gravity and cap- illary gravity water waves in two dimensions, and capillary gravity water waves in three dimensions, for any periodic fundamental domain. This is a problem in bifurcation theory, yielding curves in the two dimensional case and bifurcation surfaces in the three dimensional case. In order to address the presence of resonances, the proof is based on a variational formulation and a topological argument, which is related to the resonant Lyapunov center theorem. Key words. water waves, bifurcation theory, traveling waves AMS subject classifications. 35; 76 PII. S0036141099354181