Publication: Kink stability, propagation, and length-scale competition in the periodically modulated sine-Gordon equation
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ISSN: 1539-3755 (print version)
ISSN: 1550-2376 (online version)
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1994-05
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American Physical Society
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Abstract
We have examined the dynamical behavior of the kink solutions of the one-dimensional sineGordon
equation in the presence of a spatially periodic parametric perturbation. Our study clarifies
and extends the currently available knowledge on this and related nonlinear problems in four directions.
First, we present the results of a numerical simulation program that are not compatible
with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a
perturbative calculation that helps interpr~t those previous predictions, enabling us to understand
in depth our numerical results. Third, we apply the collective coordinate formalism to this system
and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth,
we report on the occurrence of length-scale competition in this system and show how it can be
understood by means of linear stability analysis. Finally, we conclude by summarizing the general
physical framework that arises from our study.
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Bibliographic citation
Physical Review E, vol. 49, n. 5, may 1994. Pp. 4603–4615