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

The super-rogue wave solutions of the nonlinear Schrodinger 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 Schrodinger 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. (C) 2016 Shanghai Jiaotong University. Published by Elsevier B.V.