Quasi-periodic route to chaos in a near-integrable PDE: Homoclinic crossings

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

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31 Scopus citations


A new numerical experiment is discussed which shows a quasi-periodic route to intermittent chaos - typical for near-conservative, dispersive waves of small amplitude (nonlinear Schrödinger regime) in one spatial dimension. This route has: temporally one frequency, then two, then chaos; associated spatial symmetry changes; a low dimensional intermittent strange attractor. A nonlinear spectral transform has been used to show: a small number of nonlinear modes in the chaotic state; interaction of coherent modes with radiation modes: and, most importantly, that (unperturbed) homoclinic states are crossed repeatedly in these regimes. These homoclinic states: (a) separate spatially localized modes from radiation modes, and (b) act as sources of extreme sensitivity which can produce temporal chaos: for the first time homoclinic states have been simultaneously associated with both spatial patterns and temporal chaos.

Original languageEnglish
Pages (from-to)335-340
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number6-7
StatePublished - 7 Mar 1988
Externally publishedYes


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