Local and nonlocal complex discrete and semi-discrete sine-Gordon equations and solutions

TL;DR

This paper investigates local and nonlocal complex reductions of discrete and semi-discrete sine-Gordon equations, constructing explicit solutions like solitons and Jordan blocks, and analyzing their dynamics.

Contribution

It introduces new local and nonlocal complex reductions of discrete sine-Gordon equations and constructs explicit solutions including solitons and Jordan blocks.

Findings

Explicit soliton and Jordan-block solutions are constructed.

Dynamics of 1-soliton solutions are analyzed and illustrated.

New types of reductions for discrete sine-Gordon equations are proposed.

Abstract

In this paper, local and nonlocal complex reduction of a discrete and a semi-discrete negative order Ablowitz-Kaup-Newell- Segur equations is studied. Cauchy matrix type solutions, including soliton solutions and Jordan-block solutions, for the resulting local and nonlocal complex discrete and semi-discrete sine-Gordon equations are constructed. Dynamics of 1-soliton solution are analyzed and illustrated.