Numerical study on the generation and evolution of the super-rogue waves

The super-rogue wave solutions of the nonlinear Schrödinger equation(NLS)are numerically studied based on the weakly nonlinear hydrodynamic equation.The super-rogue wave solutions up to the 5th order,also known as the so-called super-rogue waves,are observed according to the results obtained by numerically solving the modified nonlinear Schrödinger equation which is also known as the Dysthe equation that has a higher accuracy along the wave evolution in space.By using the 4th order split-step pseudo-spectral method during the integral process,more accurate results with a smaller conservation error were obtained.It is found that the super-rogue waves can be generated when considering the higher order nonlinearity.The fourth-order terms in the mNLS equation should not be ignored in numerically simulating the evolution of the super-rogue wave formation.The bound wave components also play important roles in the wave evolution.The enhancement of wave amplitude becomes larger due to the influence of bound wave components.