Formation of the rogue wave due to non-linear two-dimensional waves interaction

Abstract It is shown that generation of the rogue waves in the ocean may be described in framework of non-linear two-dimensional shallow water theory where the simplest two-dimensional long wave non-linear model corresponds to the Kadomtsev–Petviashvili (KP) equation. Numerical solution of the KP equation is obtained to account for the formation of localized abnormally high amplitude wave due to a resonant superposition of two incidentally non-interacting long-crested waves. Peculiarities of the solution allow to explain rare and unexpected appearance of the rogue waves. However, our solution differs from the exact two-solitary wave solution of the KP equation used before for the rogue waves description.