A nonlinear, parametrically driven, variable‐reluctance electroacoustic transducer

Nonlinear dynamics of a parametrically driven sine-Gordon system.

Solitons in a Parametrically Driven Damped Discrete Nonlinear Schrödinger Equation

We consider a parametrically driven damped discrete nonlinear Schrödinger (PDDNLS) equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental discrete bright solitons. We show that there are two types of onsite discrete soliton, namely onsite type I and II. We also show that there are four types of intersite discrete soliton, called int...

Intrinsic localized modes in parametrically driven arrays of nonlinear resonators.

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-L...

Pattern selection in parametrically driven arrays of nonlinear resonators.

We study the problem of pattern selection in an array of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems, using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [Phys. Rev. E 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of different wave numbers as the drive amplitude...

Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation

Faraday waves are described, under appropriate conditions, by a damped nonlocal parametrically driven nonlinear Schrödinger equation. As the strength of the applied forcing increases this equation undergoes a sequence of transitions to chaotic dynamics. The origin of these transitions is explained using a careful study of a two-mode Galerkin truncation and linked to the presence of heteroclinic...