TY - JOUR

T1 - Quasi-periodic route to chaos in a near-integrable PDE

T2 - Homoclinic crossings

AU - Bishop, A. R.

AU - McLaughlin, D. W.

AU - Forest, M. G.

AU - Overman, E. A.

PY - 1988/3/7

Y1 - 1988/3/7

N2 - 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.

AB - 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.

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U2 - 10.1016/0375-9601(88)90580-4

DO - 10.1016/0375-9601(88)90580-4

M3 - Article

AN - SCOPUS:45549115374

SN - 0375-9601

VL - 127

SP - 335

EP - 340

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 6-7

ER -