Solutions and continuum limits to nonlocal discrete sine-Gordon equations: bilinearization reduction method

TL;DR

This paper develops a bilinearization reduction method to find exact solutions for nonlocal discrete sine-Gordon equations and explores their continuum limits and soliton dynamics.

Contribution

It introduces a novel bilinearization reduction approach for nonlocal discrete sine-Gordon equations and derives their solutions and continuum limits.

Findings

Exact double Casoratian solutions for nonlocal discrete sine-Gordon equations

Continuum limits yield nonlocal semi-discrete sine-Gordon equations

Analysis of soliton dynamics and asymptotic behavior

Abstract

As with nonlocal continuous and semi-discrete integrable systems, the study of nonlocal discrete integrable systems is also of interest. In this paper, local and nonlocal reductions of a fully discrete negative order Ablowitz-Kaup-Newell-Segur equation are investigated. We give out the exact solutions in double Casoratian form to the reduced nonlocal discrete sine-Gordon equations by the bilinearization reduction method. Then, through the continuum limits, nonlocal semi-discrete sine-Gordon equations and their solutions are obtained. The dynamics of soliton solutions are analyzed and illustrated by asymptotic analysis. The research ideas and methods in this paper can be generalized to promote the studies on nonlocal discrete integrable systems.