Soliton solutions of the classical lattice sine-Gordon system

TL;DR

This paper investigates soliton solutions in a classical lattice sine-Gordon system, analyzing their behavior at infinity, scattering properties, and periodic solutions, thus advancing understanding of discrete integrable systems.

Contribution

It introduces a reduction to a top-like system and provides detailed analysis of soliton scattering and periodic solutions in the lattice sine-Gordon model.

Findings

Soliton solutions exhibit specific scattering behaviors.

The system reduces to a top-like model under certain conditions.

Periodic solutions are characterized and analyzed.

Abstract

We study the soliton-type solutions of the system introduced by B. Feigin and the author in in [EF]. We show that it reduces to a top-like system, and we study the behaviour of the solutions at the lattice infinity. We compute the scattering of the solitons and study some periodic solutions of the system.