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Intrinsic localized modes in parametrically driven arrays of nonlinear resonators

Kenig, Eyal and Malomed, Boris A. and Cross, M. C. and Lifshitz, Ron (2009) Intrinsic localized modes in parametrically driven arrays of nonlinear resonators. Physical Review E, 80 (4). Art. No. 046202 . ISSN 1539-3755. https://resolver.caltech.edu/CaltechAUTHORS:20091124-145326627

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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 Schrödinger 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevE.80.046202DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevE.80.046202 PublisherUNSPECIFIED
ORCID:
AuthorORCID
Lifshitz, Ron0000-0002-8829-5506
Additional Information:© 2009 The American Physical Society. Received 8 April 2009; revised manuscript received 13 August 2009; published 2 October 2009. We thank an anonymous referee for inquiring about the dynamical formation of solitons in our array, which prompted us to add Sec. V. This work was supported by the U.S.-Israel Binational Science Foundation (BSF) through Grant No. 2004339, and by the Israeli Ministry of Science and Technology.
Funders:
Funding AgencyGrant Number
U. S.-Israel Binational Science Foundation (BSF)2004339
Israeli Ministry of Science and TechnologyUNSPECIFIED
Subject Keywords:bound states; Ginzburg-Landau theory; localised modes; micromechanical devices; nanoelectromechanical devices; nonlinear equations; resonators; Schrodinger equation; solitons
Issue or Number:4
Classification Code:PACS: 05.45.-a; 63.20.Pw; 62.25.-g; 85.85.+j.
Record Number:CaltechAUTHORS:20091124-145326627
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20091124-145326627
Official Citation:Intrinsic localized modes in parametrically driven arrays of nonlinear resonators Eyal Kenig, Boris A. Malomed, M. C. Cross, and Ron Lifshitz, Phys. Rev. E 80, 046202 (2009), DOI:10.1103/PhysRevE.80.046202
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16796
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Dec 2009 20:17
Last Modified:09 Mar 2020 13:19

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