Coherence and chaos in the driven,damped sine-Gordon chain |
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| Authors: | D. Bennett A. R. Bishop S. E. Trullinger |
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| Affiliation: | (1) Center for Nonlinear Studies, Los Alamos National Laboratory, 87545 Los Alamos, New Mexico, USA;(2) Present address: Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, 87545 Los Alamos, New Mexico, USA;(3) Institute for Theoretical Physics, University of California, 93106 Santa Barbara, California, USA;(4) Department of Physics, University of Southern California, 90007 Los Angeles, California, USA;(5) Institute for Theoretical Physics, University of California, 93106 Santa Barbara, California, USA;(6) Present address: Physics Department, Stanford University, 94305 Stanford, CA, USA |
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| Abstract: | Representative example of preliminary numerical results are presented for solutions of the deterministic sine-Gordon equation under the influence of damping and a sinusoidal uniform driving force. Depending on the choice of (inhomogeneous) initial conditions and values of the amplitude and frequency of the driving force, we find a great variety of possible responses, including: (i) permanent spatial structures riding on an overall background motion which can be temporally chaotic or not, (ii) intermittent transitions between at least two metastable spatial structures which are typically a localized breather-like structure and an extended wave train, in the presence of temporal chaos or not and with large- or small-amplitude background motion. For some parameter values, we find very similar power spectra for different initial conditions, while other cases show considerable dependence on initial conditions. Both the spatial and temporal behavior of the response can exhibit extreme sensitivity to small changes in the parameters. |
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