RT Journal Article
T1 Length-scale competition in the damped sine-Gordon chain with spatiotemporal periodic driving
A1 Cai, David
A1 Bishop, Alan R.
A1 Sánchez, Angel
AB It is shown that there are two different regimes for the damped sine-Gordon chain driven by thespatiotemporal periodic force rsin(wt - knx) with a flat initial condition. For w > kn, the systemfirst bifurcates at a critical re (n) to a translating two-breather excitation from a state locked to thedriver. For w < kn, the excitations of the system are the locked states with the phase velocity w/knin all the regions of r studied. In the first regime, the frequency of the breathers is controlled byw, and the velocity of the breathers, controlled by kn, is shown to be the group velocity determinedfrom the linear dispersion relation for the sine-Gordon equation. A linear stability analysis revealsthat, in addition to two competing length scales, namely, the width of the breathers and the spatialperiod of the driving, there is one more length scale which plays an important role in controllingthe dynamics of the system at small driving. In the second regime the length scale kn controlsthe excitation. The above picture is further corroborated by numerical nonlinear spectral analysis.An energy-balance estimate is also presented and shown to predict the critical value of r in goodagreement with the numerical simulations.
PB American Physical Society
SN 1539-3755 (print version)
SN 1550-2376 (online version)
YR 1993
FD 1993-08
LK https://hdl.handle.net/10016/15102
UL https://hdl.handle.net/10016/15102
LA eng
NO We acknowledge support for this work by the V.S. DOE and partial financial support for A.S. by CICyT (Spain) under Project No. MAT90-0544.
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RD 1 sept. 2024