Length-scale competition in the damped sine-Gordon chain with spatiotemporal periodic driving

David Cai, A. R. Bishop, Angel Sanchez

Research output: Contribution to journalArticle

Abstract

It is shown that there are two different regimes for the damped sine-Gordon chain driven by the spatiotemporal periodic force sin(t-knx) with a flat initial condition. For >kn, the system first bifurcates at a critical c(n) to a translating two-breather excitation from a state locked to the driver. For <kn, the excitations of the system are the locked states with the phase velocity /kn in all the regions of studied. In the first regime, the frequency of the breathers is controlled by, and the velocity of the breathers, controlled by kn, is shown to be the group velocity determined from the linear dispersion relation for the sine-Gordon equation. A linear stability analysis reveals that, in addition to two competing length scales, namely, the width of the breathers and the spatial period of the driving, there is one more length scale which plays an important role in controlling the dynamics of the system at small driving. In the second regime the length scale kn controls the 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 in good agreement with the numerical simulations.

Original languageEnglish (US)
Pages (from-to)1447-1452
Number of pages6
JournalPhysical Review E
Volume48
Issue number2
DOIs
StatePublished - 1993

Fingerprint

Breathers
Damped
Length Scale
Excitation
excitation
translating
phase velocity
group velocity
spectrum analysis
Phase Velocity
Sine-Gordon Equation
Group Velocity
Linear Relation
Energy Balance
Linear Stability Analysis
Dispersion Relation
Spectral Analysis
Nonlinear Analysis
Driver
Critical value

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Length-scale competition in the damped sine-Gordon chain with spatiotemporal periodic driving. / Cai, David; Bishop, A. R.; Sanchez, Angel.

In: Physical Review E, Vol. 48, No. 2, 1993, p. 1447-1452.

Research output: Contribution to journalArticle

Cai, David ; Bishop, A. R. ; Sanchez, Angel. / Length-scale competition in the damped sine-Gordon chain with spatiotemporal periodic driving. In: Physical Review E. 1993 ; Vol. 48, No. 2. pp. 1447-1452.
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