Conservative Fourier spectral method for a class of modified Zakharov systems with high-order space fractional quantum correction $\dagger$

Abstract

In this paper, we consider the Fourier spectral method and numerical investigation for a class of modified Zakharov systems with high-order space fractional quantum correction. First, the Fourier spectral scheme of the system is developed with periodic boundary condition based on the Crank-Nicolson/leap-frog methods in time and the Fourier spectral method in space. Moreover, it is shown that the scheme preserves simultaneously mass and energy conservation laws. Second, we analyze stability and convergence of the numerical scheme. Last, the numerical experiments are given, and the results show the correctness of theoretical results and the efficiency of the conservative scheme.