Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators

TL;DR

This paper investigates the formation, stability, and interactions of intrinsic localized modes in arrays of nonlinear resonators, using a derived amplitude equation to predict behaviors relevant to MEMS and NEMS devices.

Contribution

The study derives a nonlinear Schroedinger equation with nonlinear damping from the equations of motion, providing new insights into ILMs in driven resonator arrays.

Findings

ILMs can form bound states

ILMs can split into two under certain conditions

Simulations confirm theoretical predictions

Abstract

We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schroedinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory.