Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

TL;DR

This paper investigates how Kac-Baker long-range interactions influence kink properties in the discrete sine-Gordon model, revealing effects on kink width, localization, internal modes, and radiation behavior.

Contribution

It provides a detailed analysis of how long-range dispersive interactions alter kink dynamics and internal modes in the discrete sine-Gordon model, highlighting new phenomena.

Findings

Kink width increases with LRI range only under strong coupling.

Kinks become localized below a critical coupling value.

LRI induces internal localized and quasilocalized modes.

Abstract

We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of strong interparticle coupling. On the contrary, the kink becomes intrinsically localized if the coupling is under some critical value. Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI increases for supercritical values of the coupling but remains finite for subcritical values. We demonstrate that LRI essentially transforms the internal dynamics of the kinks, specifically creating their internal localized and quasilocalized modes. We also show that moving kinks radiate plane waves due to break of the Lorentz invariance by LRI.