We consider specific features of the formation of localized surface waves at the interface between linear dielectric and photorefractive crystals with a nonlocal diffusion component of nonlinear response. Profiles of the surface waves are numerically found and guiding properties of the surface are investigated. Stability of the obtained surface waves is considered and it is shown that the well-...

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D poten...

Two-dimensional nonlinear models are developed to account for abnormal surface ocean waves generation and propagation. These models are based on the KadomtsevPetviashvili equation, the 2D Benjamin-Ono equation and the 2D Gardner equation. Possible mechanisms of the waves formation suggested are the resonant interaction between semi-plane waves or waves with curved fronts or the transverse insta...

We study the long-time evolution of deep-water ocean surface waves in order to better understand the behavior of the nonlinear interaction processes that need to be accurately predicted in numerical models of wind-generated ocean surface waves. Of particular interest are those nonlinear interactions which are predicted by weak turbulence theory to result in a wave energy spectrum of the form of...

We present a new hybrid asymptotic-numerical method to study nonlinear wave-body interaction in threedimensional water of arbitrary depth. After solving a simplified body problem numerically using a distribution of singularities along the body surface, we reduce the nonlinear free surface problem to a closed system of two nonlinear evolution equations, using a systematic asymptotic expansion, f...