Stability of mode-locked kinks in the ac driven and damped sine-Gordon lattice

TL;DR

This paper investigates the stability of mode-locked kinks in a driven, damped sine-Gordon lattice, revealing how bifurcations affect stability and showing enhanced stability in the overband frequency regime.

Contribution

It provides a detailed analysis of mode-locked kink stability in the overband regime using Floquet theory, highlighting differences from low-frequency cases.

Findings

Mode-locked kink states destabilize via Hopf or tangential bifurcations.

Standing mode-locked kinks are stable at much higher amplitudes in the overband case.

Stability persists at bias amplitudes an order of magnitude larger than in low-frequency regimes.

Abstract

Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice that is driven by the oscillating force is studied. The investigation is focused mostly on the properties of the mode-locked states in the {\it overband} case, when the driving frequency lies above the linear band. With the help of Floquet theory it is demonstrated that the destabilizing of the mode-locked state happens either through the Hopf bifurcation or through the tangential bifurcation. It is also observed that in the overband case the standing mode-locked kink state maintains its stability for the bias amplitudes that are by the order of magnitude larger than the amplitudes in the low-frequency case.