Numerical study of the generation and evolution of breather-type rogue waves

The behaviour of the Peregrine breather-type rogue waves is numerically studied based on the fourth-order nonlinear Schrödinger equation. The wavelet analysis method is adopted in order to analyse the time-frequency energy distribution during the generation and evolution of the Peregrine breather. It shows that the peak of the largest amplitudes of the resulting waves can be described in terms of the Peregrine breather-type solution and leads to the solution of the nonlinear Schrödinger (NLS) equation. Meanwhile, strong energy density is found to surge instantaneously and be seemingly carried over to the high-frequency components at the instant when the large, rogue wave occurs.