三维非线性Schroedinger方程的拟谱算法
Pseudospectral Algorithms for Solving Nonlinear Schroedinger Equation in 3D
摘要：
本文介绍了数值求解一维、二维和三维含时非线性Schroedinger方程的三种拟谱算法（Euler、Leapfrog和Zeroz）。在参数空间中的数值稳定区域确定的立方非线性，它可以很容易地扩展到其他非线性。对于前两个算法，稳定性的最大时间步长计算的最大傅立叶谐波承认的频谱方法用于计算空间导数。如果使用离散傅立叶变换，即对于周期性边界条件，则公式是直接适用的。这些公式已用于本课题组编制的相应数值程序中。
英文摘要：
Three pseudospectral algorithms are described (Euler, leapfrog and trapez) for solving numerically the time dependent nonlinear Schroedinger equation in one, two or three dimensions. Numerical stability regions in the parameter space are determined for the cubic nonlinearity, which can be easily extended to other nonlinearities. For the first two algorithms, maximal timesteps for stability are calculated in terms of the maximal Fourier harmonics admitted by the spectral method used to calculate space derivatives. The formulas are directly applicable if the discrete Fourier transform is used, i.e. for periodic boundary conditions. These formulas were used in the relevant numerical programs developed in our group.
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