New compact equation for numerical simulation of freak waves on deep water

Considering surface gravity waves which propagate in same direction we applied canonical transformation to a water wave equation and drastically simplify the Hamiltonian. After this transformation, corresponding equation of motion is written in x-space in a compact form. This new equation is suitable for analytical studies and numerical simulations. Localized in space breather-type solution was found numerically by using iterative Petviashvili method. Numerical simulation of breathers collision shows the stability of such solutions. We observed the freak wave formation in numerical simulations of sea surface waving in the framework of new equation. (paper)