In this paper, a high-accuracy conservative difference scheme is presented for solving the space fractional Zakharov system, which preserves the original conservative properties. By virtue of the standard energy method and mathematical induction, it is shown that the proposed scheme possesses the convergence rates of $\mathcal{O}({\tau }^2+h^4)$. Finally, numerical examples testify the effectiveness of the conservative difference scheme and demonstrate the correctness of theoretical results. In particular, the effects of the fractional order α and β on the solitary solution behaviours are shown clearly through many intuitionistic images.

中文翻译：

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分数Zakharov系统的保守差分格式及收敛性分析

本文提出了一种求解空间分数Zakharov系统的高精度保守差分方案，该方案保留了原有的保守性质。借助标准能量法和数学归纳法，表明所提出的方案具有收敛速度为$\mathcal{哦}({\tau }^2+H^4)$. 最后，数值算例验证了保守差分方案的有效性，证明了理论结果的正确性。特别是，分数阶α和β对孤解行为的影响通过许多直观的图像清楚地显示出来。