| Gravity-Capillary waves are free surface wave at a lengthscale where the forces due to gravity and surface tension are both important, approximately one centimeter for an air-water interface. At this lengthscale the phase speed of linear waves has a minimum, about which waves are locally nondispersive. The classic system for studying gravity-capillary waves is the equations of potential flow. These equations have localized, solitary, traveling wave solutions. As a system for studying the dynamic properties of these waves, the potential flow equations are computationally expensive. In this work, a number of weakly nonlinear model equations for gravity-capillary waves will be developed. These models are compared, and the dynamics of solitary waves in each model are examined. The stability of solitary waves is studied, via linear stability analysis and numerical time evolution. The dependence of the waves speed on wave energy is examined; a result is presenting connecting the wave's energy and its stability. Solitary wave collisions are also examined. The connection between solitary waves in model equations and those in the associated Nonlinear Schrodinger Equation is investigated. |
