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Equilibrium states and chaos in an oscillating double-well potential

Jiang, H and Susanto, H and Benson, TM and Cliffe, KA (2014) 'Equilibrium states and chaos in an oscillating double-well potential.' Physical Review A - Atomic, Molecular, and Optical Physics, 89 (1). ISSN 1050-2947

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Abstract

We investigate numerically parametrically driven coupled nonlinear Schrödinger equations modeling the dynamics of coupled wave fields in a periodically oscillating double-well potential. The equations describe, among other things, two coupled periodically curved optical waveguides with Kerr nonlinearity or Bose-Einstein condensates in a double-well potential that is shaken horizontally and periodically in time. In particular, we study the persistence of equilibrium states of the undriven system due to the presence of the parametric drive. Using numerical continuations of periodic orbits and calculating the corresponding Floquet multipliers, we find that the drive can (de)stabilize a continuation of an equilibrium state indicated by the change in the (in)stability of the orbit, showing that parametric drives can provide a powerful control to nonlinear (optical- or matter-wave-) field tunneling. We also discuss the appearance of chaotic regions reported in previous studies that is due to destabilization of a periodic orbit. Analytical approximations based on an averaging method are presented. Using perturbation theory, the influence of the drive on the symmetry-breaking bifurcation point is analyzed. © 2014 American Physical Society.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 12 Nov 2014 19:28
Last Modified: 30 Jan 2019 16:18
URI: http://repository.essex.ac.uk/id/eprint/11549

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