A quasi-periodic route to chaos in a near-integrable pde

A. R. Bishop, M. G. Forest, D. W. McLaughlin, E. A. Overman

Research output: Contribution to journalArticle

Abstract

Pattern formation and transitions to chaos are described for the damped, ac-driven, one-dimensional, periodic sine-Gordon equation. In a nonlinear Schrödinger regime, a generic quasi-periodic route to intermittent chaos is exhibited in detail using a range of dynamical systems diagnostics. In addition, a nonlinear spectral transform is exploited: (i) to identify and quantify coordinates of space-time attractors in terms of a small number of soliton modes of the underlying integrable system; (ii) to use these analytic coordinates to identify homoclinic orbits as possible sources of chaos; and (iii) to demonstrate the significance of energy transfer between coherent and extended states in this chaotic system.

Original languageEnglish (US)
Pages (from-to)293-328
Number of pages36
JournalPhysica D: Nonlinear Phenomena
Volume23
Issue number1-3
DOIs
StatePublished - 1986

Fingerprint

Chaos theory
chaos
Chaos
routes
sine-Gordon equation
Sine-Gordon Equation
Chaotic systems
Homoclinic Orbit
Energy Transfer
Integrable Systems
Pattern Formation
Solitons
Damped
dynamical systems
Energy transfer
Chaotic System
Attractor
Diagnostics
Dynamical systems
Orbits

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

A quasi-periodic route to chaos in a near-integrable pde. / Bishop, A. R.; Forest, M. G.; McLaughlin, D. W.; Overman, E. A.

In: Physica D: Nonlinear Phenomena, Vol. 23, No. 1-3, 1986, p. 293-328.

Research output: Contribution to journalArticle

Bishop, A. R. ; Forest, M. G. ; McLaughlin, D. W. ; Overman, E. A. / A quasi-periodic route to chaos in a near-integrable pde. In: Physica D: Nonlinear Phenomena. 1986 ; Vol. 23, No. 1-3. pp. 293-328.
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