In this paper, an efficient finite difference scheme is proposed for one dimension and two dimension coupled space fractional nonlinear Schrödinger equations. First, the high-order difference scheme and Crank–Nicolson scheme are used to one dimension coupled space fractional nonlinear Schrödinger equations. second, we show that the high-order conservative difference scheme satisfies the mass and energy conservation laws respectively, and convergence and unconditional stability of the scheme are also proved. Next, we give the high-order conservative scheme for two dimension coupled space fractional nonlinear Schrödinger equations. Finally, some numerical results are reported to verify our theoretical analysis.

本文针对一维和二维耦合空间分数非线性薛定谔方程提出了一种有效的有限差分格式。首先，将高阶差分格式和Crank-Nicolson格式用于一维耦合空间分数非线性薛定谔方程。其次，我们证明了高阶保守差分格式分别满足质量和能量守恒定律，并且证明了该格式的收敛性和无条件稳定性。接下来，我们给出了二维耦合空间分数非线性薛定谔方程的高阶保守格式。最后，报告了一些数值结果来验证我们的理论分析。