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中文摘要：
讨论一维和二维非线性Schrdinger（NLS）方程的数值求解.基于扩散广义黎曼问题的数值流量,构造一种直接间断Galerkin方法（DDG）求解非线性Schrdinger方程.证明该方法L2稳定性,并说明DDG格式是一种守恒的数值格式.对一维NLS方程的计算表明,DDG格式能够模拟各种孤立子形态,而且可以保持长时间的高精度.二维NLS方程的数值结果显示该方法的高精度和捕捉大梯度的能力.
英文摘要：
We discuss numerical simulation of one-and two-dimensional nonlinear Schrdinger（NLS） equations（NLS）.With numerical flux of diffusive generalized Riemann problem,a direct discontinuous Galerkin（DDG） method is proposed.L2 stability of the DDG scheme is proved and it is shown that it is a conservative numerical scheme.The one-dimensional case indicates that the DDG scheme simulates various kinds of soliton propagations and it has excellent long-time numerical behaviors.Two-dimensional numerical results demonstrate that the method has high accuracy and is capable of capturing strong gradients.
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