Publication: Resonances in the dynamics of Ø4 kinks perturbed by ac forces
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ISSN: 1539-3755 (print version)
ISSN: 1550-2376 (online version)
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2000-10
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American Physical Society
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Abstract
We study the dynamics of Ø4 kinks perturbed by an ac force, both with and without damping. We address
this issue by using a collective coordinate theory, which allows us to reduce the problem to the dynamics of the
kink center and width. We carry out a careful analysis of the corresponding ordinary differential equations, of
Mathieu type in the undamped case, finding and characterizing the resonant frequencies and the regions of
existence of resonant solutions. We verify the accuracy of our predictions by numerical simulation of the full
partial differential equation, showing that the collective coordinate prediction is very accurate. Numerical
simulations for the damped case establish that the strongest resonance is the one at half the frequency of the
internal mode of the kink. In conclusion, we discuss the possible relevance of our results for other systems,
especially the sine-Gordon equation. We also obtain additional results regarding the equivalence between
different collective coordinate methods applied to this problem.
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Physical Review E, vol. 62, n. 4, oct. 2000. Pp. 5695–5705