A linear decoupled physical-property-preserving difference method for fractional-order generalized Zakharov system

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 physicalproperty-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(Delta t(2) + h(4)) in discrete L-infinity and L-2 norms. The main feature of the new scheme is physical-propertypreserving, 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. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, an efficient physical-property-preserving algorithm is proposed and analyzed for the space fractional-order generalized Zakharov system. The system is reformulated as an equivalent system of equations by introducing the auxiliary equation. A spatial fourth-order physical-property-preserving linearly implicit difference scheme is developed for the transformed system. The scheme is proven to have the optimal order of O(Delta t(2) + h(4)) in discrete L-infinity and L-2 norms through the use of a cut-off function and discrete energy analysis method. The scheme is characterized by its physical-property preservation, linear decoupling, and suitability for parallel computing, especially in long time simulations and large-scale problems. Ample numerical results are provided to demonstrate the efficiency and preservation properties of the scheme, as well as investigate the dynamic behaviors of different solitary waves. (c) 2023 Elsevier B.V. All rights reserved.