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 - Dec 1986

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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