Abstract
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.
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