Two-dimensional long wave nonlinear models for the rogue waves in the ocean

Two-dimensional long wave nonlinear models are developed to describe the propagation of the rogue waves. It is shown that the simplest model corresponds to the Kadomtsev-Petviashvili equation, while the influence of the atmosphere movement and the current in the ocean on the generation of the rogue waves is resulted in derivation of new nonlinear integro-differential equation. Two mechanisms of the rogue wave formation are proposed on. the basis of the model equations. First is based on a resonant interaction of inclined plane solitary waves. According to the second one the rogue wave is single two-dimensionally localized travelling wave having the pit shape.