Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators
arXiv:0904.1355 · doi:10.1103/PhysRevE.80.046202
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.
New version contains a new section discussing the dynamical formation of solitons and the stability of non-zero uniform states
References in corpus (24)
- Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array
- Observation of breathers in Josephson ladders
- Experimental Generation and Observation of Intrinsic Localized Spin Wave Modes in an Antiferromagnet
- Noise-enabled precision measurements of a Duffing nanomechanical resonator
- Superconducting Qubit Storage and Entanglement with Nanomechanical Resonators
- Metastability and the Casimir Effect in Micromechanical Systems
- Response of parametrically-driven nonlinear coupled oscillators with application to micro- and nanomechanical resonator arrays
- Synchronization by Nonlinear Frequency Pulling
- Basins of attraction of a nonlinear nanomechanical resonator
- Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator
- Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators
- A Potential of Interaction between Two- and Three-Dimensional Solitons
- Optical manipulation of intrinsic localized vibrational energy in cantilever arrays
- Mechanical Mixing in Nonlinear Nanomechanical Resonators
- Secondary Instabilities and Spatiotemporal Chaos in Parametric Surface Waves
- Synchronization by Reactive Coupling and Nonlinear Frequency Pulling
- Travelling solitons in the parametrically driven nonlinear Schroedinger equation
- Classical to quantum transition of a driven nonlinear nanomechanical resonator
- Nonlinear response and discrete breather excitation in driven micro-mechanical cantilever arrays
- Driven Intrinsic Localized Modes in a Coupled Pendulum Array
- Response of discrete nonlinear systems with many degrees of freedom
- Pattern selection in parametrically-driven arrays of nonlinear resonators
- Driven localized excitations in the acoustic spectrum of small nonlinear macroscopic and microscopic lattices
- Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation
Cited by in corpus (28)
- Localized Breathing Modes in Granular Crystals with Defects
- Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
- Persistent coherent beating in coupled parametric oscillators
- Theory of coupled parametric oscillators beyond coupled Ising spins
- Excitation of coupled phononic frequency combs via two-mode parametric three-wave mixing
- Soliton complexity in the damped-driven nonlinear Schrödinger equation: stationary, periodic, quasiperiodic complexes
- Discrete solitons in electromechanical resonators
- Experimental observation of the bifurcation dynamics of an intrinsic localized mode in a driven 1-D nonlinear lattice
- Exact solutions for discrete breathers in forced-damped chain
- Solitary vortices supported by localized parametric gain
- Pinned modes in lossy lattices with local gain and nonlinearity
- Solitons supported by localized parametric gain
- Discrete Breathers and Multi-Breathers in Finite Vibro-Impact Chain
- Homoclinic orbits and chaos in a pair of parametrically-driven coupled nonlinear resonators
- A quasi-periodic route to chaos in a parametrically driven nonlinear medium
- Generation and propagation of topological solitons in a chain of coupled parametric-micromechanical-resonator arrays
- Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity
- Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media
- Dynamics of impurity attraction and repulsion of an intrinsic localized mode in a driven 1-D cantilever array
- Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
- Drift instabilities in localised Faraday patterns
- Collapse dynamics for the discrete nonlinear Schrödinger equation with gain and loss
- Self-trapped leaky waves in lattices: discrete and Bragg soleakons
- Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schrödinger equation: justification and numerical comparisons
- Localization in finite asymmetric vibro-impact chains
- Mini-review: Spatial solitons supported by localized gain
- Localization in Coupled Finite Vibro-Impact Chains: Discrete Breathers and Multibreathers
- Logic Operations Demonstrated with Localized Vibrations in a Micromechanical Cantilever Array