Formation of abnormally high localized waves due to nonlinear two-dimensional waves interaction

It is shown that the simplest two-dimensional Iong wave nonlinear model for the propagation of the rogue waves corresponds to the Kadomtsev-Petviashvili (KP) equation. The mcchanism of the rogue wave formation is suggestcd based on a resonant head-on collision of two plane incidentally non-interacting waves. Corresponding numerical solotion of the KP equation is obtained to account €or the formation of localized abnornially high amplitude wave. Peculiarities of the solution allows to explain rare but unexpected appearance of the rogue waves. The shape of the steady state of the solution differs from khat of the exact two-soliton solution of the tip equation.