In this paper, we solve the nonlinear space fractional complex Ginzburg-Landau equations. The motivation of this work is to give a fast numerical method to solve the linear system, which is obtained from the nonlinear space fractional complex Ginzburg-Landau equations. The coefficient matrix of the linear system is the sum of a complex diagonal matrix and a real Toeplitz matrix. The significance of this work is that the new method has a superiority in computation because we can use the circulant preconditioner and the fast Fourier transform to solve the linear system. Numerical examples are tested to illustrate the advantage of the numerical method.

在本文中，我们求解非线性空间分数复数 Ginzburg-Landau 方程。这项工作的动机是提供一种快速数值方法来求解线性系统，该方法是从非线性空间分数复数 Ginzburg-Landau 方程获得的。线性系统的系数矩阵是复数对角矩阵和实数托普利茨矩阵之和。这项工作的意义在于新方法在计算上具有优势，因为我们可以使用循环预处理器和快速傅立叶变换来求解线性系统。数值例子被测试以说明数值方法的优点。