Discrete solitons in electromechanical resonators

TL;DR

This paper analyzes the stability of discrete solitons in a parametrically driven Klein-Gordon system modeling micro- and nano-devices, revealing how parametric driving influences soliton stability.

Contribution

It introduces a multiscale reduction to a discrete nonlinear Schrödinger equation and demonstrates how parametric driving can stabilize or destabilize various solitons.

Findings

Parametric driving can stabilize intersite bright and dark solitons.

Dark solitons can be stable over a range of driving coefficients.

Numerical simulations confirm analytical stability predictions.

Abstract

We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrodinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein--Gordon system through the discrete Schrodinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discrete solitons and onsite and intersite dark solitons. Most importantly, we show that there is a range of values of the driving coefficient for which dark solitons are stable, for any value of the coupling constant, i.e. oscillatory instabilities are totally suppressed. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results. Numerical integrations of the Klein--Gordon equation are performed, confirming the relevance of our analysis.