Abstract
In this paper, an efficient physical-property-preserving algorithm for the space fractional-order generalized Zakharov system is proposed and analyzed. Firstly, the space fractional-order generalized Zakharov system is reformulated as an equivalent system of equations by introducing the auxiliary equation. Then the spatial fourth-order physical-property-preserving linearly implicit difference scheme is developed for the transformed system. Subsequently, with the aid of the cut-off function and discrete energy analysis method, the underlying scheme are proven to be with the optimal order of O(Δt2+h4) in discrete L∞ and L2 norms. The main feature of the new scheme is physical-property-preserving, linearly decoupled and easy to be applied in parallel computing, especially in long time simulations and large-scale problems. At last, ample numerical results are exhibited to substantiate the efficiency and preservation properties of our scheme, and investigate the dynamic behaviors of the collision of different solitary waves with subsonic and supersonic propagation speeds, respectively.
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