Nonlinear gravity and capillary-gravity waves

This review deals primarily with the bifurcation, stability, and evolution of gravity and capillary-gravity waves. Recent results on the bifurcation o f various types of capillary-gravity waves, including two-dimensional solit ary waves at the minimum of the dispersion curve, are reviewed. A survey of various mechanisms (including the most recent ones) to explain the frequen cy downshift phenomenon is provided. Recent significant results are given o n "horseshoe" patterns, which are three-dimensional structures observable o n the sea surface under the action of wind or in wave tank experiments. The so-called short-crested waves are then discussed. Finally, the importance of surface tension effects on steep waves is studied.