高阶呼吸子式畸形波波形的数值研究

畸形波是一种波高极大的罕见波浪,对海洋平台的结构以及工作人员的人身安全具有极大威胁。由于在开阔海域中对畸形波的观测存在困难,通过数值手段对其波形进行研究具有十分重要的意义。四阶非线性薛定谔方程又被称为Dysthe方程,能够更加准确地描述波浪的非线性演化。该文通过数值求解Dysthe方程,研究了三阶非线性薛定谔方程的高阶呼吸子解(最高至5阶解)的演化过程。提出了四阶离散步长—虚拟波谱法,得到了具有更高守恒精度的数值解。同时,通过坐标变换以及拟合对高阶呼吸子式畸形波的波形进行了深入研究。

Numerical Study of the Shapes of the Super-Rogue Waves

Rogue wave is a type of very rare and extremely large wave which will cause significant harm to the on-board staff and valuable property. It is also of significance to study the profile of such ex-treme event due to the lack of the observations in the open sea. In this paper, the performance of the higher-order rational solutions of the NLS equation 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 modi-fied nonlinear Schr?dinger 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. Shapes of such super-rogue waves were analyzed by adoption of the conversion of coordinates and interpolation.