Focusing of nonlinear wave groups in deep water

The freak wave phenomenon in the ocean is explained by the nonlinear dynamics of phase modulated wave trains. It is shown that the preliminary quadratic phase modulation of wave packets leads to the significant amplification of the «usual» modulation (Benjamin–Feir) instability. Physically, the phase modulation of water waves may be due to a variable wind in storm areas. The well-known breather solutions of the cubic Schrodinger equation appear on the final stage of the nonlinear dynamics of the wave packets, when the phase modulation becomes more uniform.