Conservative linearly-implicit difference scheme for a class of modified Zakharov systems with high-order space fractional quantum correction

Abstract

In this paper, numerical methods for the modified Zakharov system with high-order fractional Laplacian and a quantum correction (FMZS) are considered. A conservative linearly-implicit difference scheme for the FMZS is proposed. This scheme is shown to conserve the mass and energy in the discrete level. On the basis of some priori estimates and Sobolev norm inequalities, it is proven that the difference scheme is stable and convergent of order O(τ2+h2) in the maximum norm. Numerical examples are given to demonstrate the theoretical results. In particular, some complex dynamical behaviors including pattern dynamics are observed and analyzed in the numerical results.