On the internal modes in sine-Gordon chain

TL;DR

This paper investigates the internal vibrational modes of kinks in a discrete sine-Gordon chain, focusing on how antisymmetric mode frequencies influence the spectrum of nonlocalized waves and spectrum peculiarities.

Contribution

It provides a detailed analysis of the antisymmetric internal mode frequency dependence and its impact on the quasicontinuum spectrum in discrete sine-Gordon systems.

Findings

Antisymmetric mode frequency dependence affects the spectrum of nonlocalized waves.

Spectrum peculiarities occur when the antisymmetric mode frequency re-enters the continuous spectrum.

The study clarifies how discreteness and system size influence internal mode behavior.

Abstract

We address the issue of internal modes of a kink of a discrete sine-Gordon equation. The main point of the present study is to elucidate how the antisymmetric internal mode frequency dependence enters the quasicontinuum spectrum of nonlocalized waves. We analyze the internal frequency dependencies as functions of both the number of cites and discreteness parameter and explain the origin of spectrum peculiarity which arises after the frequency dependence of antisymmetric mode returns back to the continuous spectrum at some nonzero value of the intersite coupling.