In this paper, we investigate local and nonlocal reductions of a discrete negative order Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, we construct exact solutions in double Casoratian form to the reduced nonlocal discrete sine-Gordon equations. Then, nonlocal semidiscrete sine-Gordon equations and their solutions are obtained through the continuum limits. The dynamics of soliton solutions are analyzed and illustrated by asymptotic analysis. The research ideas and methods in this paper can be generalized to other nonlocal discrete integrable systems.

中文翻译：

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非局部离散正弦-戈登方程的解和连续极限：双线性化约简法

在本文中，我们研究了离散负阶 Ablowitz–Kaup–Newell–Segur 方程的局部和非局部约简。通过双线性化约简法，我们构造了约简非局部离散正弦-戈登方程的双Casoratian 形式的精确解。然后，通过连续极限得到非局部半离散sine-Gordon方程及其解。通过渐近分析对孤子解的动力学进行了分析和说明。本文的研究思路和方法可以推广到其他非局部离散可积系统。