Dynamics of Three-Dimensional Gravity-Capillary Solitary Waves in Deep Water

A model equation for gravity-capillary waves in deep water is proposed. This model is a quadratic approximation of the deep water potential flow equations, and has wavepacket-type solitary wave solutions. The model equation supports traveling solutions which decay in the propagation direction only, line solitary waves, and also in both directions, lump solitary waves. Branches of both line and lump solitary waves are computed via a numerical continuation method. The stability of each type of wave is examined. The transverse instability of line solitary waves is predicted by a similar instability of line solitary waves in the Nonlinear Schr¨odinger equation. The spectral stability of lumps is predicted using the waves’ speed energy relation. The role of wave collapse in the stability of these waves is also examined. Numerical time evolution is used to confirm stability predictions and observe dynamics, including instabilities and solitary wave collisions. Key words. water wave, sol...

• Type: Journal
• Year: 2010
• Where: SIAMAM
• Authors: Benjamin Akers, Paul A. Milewski
• Keywords: Line Solitary Waves, SIAMAM 2010, Solitary Wave, Wave