中文摘要：

用辛Runge-Kutta谱方法研究变系数非线性Schrodinger方程．我们在空间方向用快速Fourier变换方法来离散二阶导数项，在时间方向用2级4阶隐式辛Runge-Kutta方法来离散一阶导数项，给出了变系数的非线性Schrodinger方程的数值解法．数值结果显示该算法行之有效，它可以保持系统模方守恒和能量守恒的性质．

英文摘要：

We present a symplectic Runge-Kutta spectral method for nonlinear Schrodinger equations with varying coefficients, and we develop the numerical method by using 2-stage 4-order implicit symplectic Runge-Kutta method in temporal direction and fast Fourier transform method in spatial direction. Numerical results show that the algorithm is very effective in that it can preserve the global energy and the norm well.