Static Properties of the Multiple-Sine-Gordon Systems

TL;DR

This paper explores the static properties, solutions, and stability of the multiple-Sine-Gordon systems, generalizing the sine-Gordon model and analyzing their physical and mathematical characteristics.

Contribution

It introduces a comprehensive analysis of the static solutions, phase diagrams, and stability of the generalized multiple-Sine-Gordon systems, extending understanding beyond the classical sine-Gordon model.

Findings

Periodic and step-like solutions are characterized using energy density and pressure.

Short wavelength solutions are found to be linearly stable.

Solutions can be interpreted as an interacting many-body system with kink-like particles.

Abstract

In this paper, we examine some basic properties of the multiple-Sine-Gordon (MSG) systems, which constitute a generalization of the celebrated sine-Gordon (SG) system. We start by showing how MSG systems can be viewed as a general class of periodic functions. Next, periodic and step-like solutions of these systems are discussed in some details. In particular, we study the static properties of such systems by considering slope and phase diagrams. We also use concepts like energy density and pressure to characterize and distinguish such solutions. We interpret these solutions as an interacting many body system, in which kinks and antikinks behave as extended particles. Finally, we provide a linear stability analysis of periodic solutions which indicates short wavelength solutions to be stable.