Solutions and continuum limits to nonlocal discrete sine‐Gordon equations: Bilinearization reduction method

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