Numerical simulation and mechanism analysis of freak waves

A numerical wave model based on the modified fourth-order nonlinear Schroe dinger equation （mNLSE） in deep water was developed to simulate the formation of freak waves and a standard split - step, pseudo-spectral method was used to solve the equation. The validation of the model is firstly verified, then the simulation of freak waves was performed by changing sideband conditions, and the variation of wave energy was also analyzed in the evolution. The results indicate that Benjamin - Feir instability （ sideband instability） is an important mechanism for freak wave formation.

时域有限差分法计算薛定谔方程中的数值稳定性条件

对于量子力学中的时域有限差分法,往往基于经验来确定其数值稳定性条件即空间和时间增量必须满足的关系。文章从含时薛定谔波动方程出发,结合物理问题中的实际条件,推导出了空间和时间增量必须满足的数值稳定性条件。特别讨论了在不同势能的情况下该稳定性条件的适用形式,得到了适用于各种维数的统一表达式。并进一步运用时域有限差分法计算得到的数值结果说明了该稳定性条件的合理性和有效性。