dorsal/arxiv
View SchemaKink stability, propagation, and length scale competition in the periodically modulated sine-Gordon equation
| Authors | Angel Sanchez, A R Bishop, Francisco Dominguez-Adame |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9401005 |
| URL | https://arxiv.org/abs/patt-sol/9401005 |
| DOI | 10.1103/PhysRevE.49.4603 |
Abstract
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon 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 which are not compatible with the existence of a radiative threshold, predicted by earlier calculations. Second, we carry out a perturbative calculation which helps interpret 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 accurately reproduces the observed kink dynamics. Fourth, we report on a novel 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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"abstract": "We have examined the dynamical behavior of the kink solutions of the\none-dimensional sine-Gordon equation in the presence of a spatially periodic\nparametric perturbation. Our study clarifies and extends the currently\navailable knowledge on this and related nonlinear problems in four directions.\nFirst, we present the results of a numerical simulation program which are not\ncompatible with the existence of a radiative threshold, predicted by earlier\ncalculations. Second, we carry out a perturbative calculation which helps\ninterpret those previous predictions, enabling us to understand in depth our\nnumerical results. Third, we apply the collective coordinate formalism to this\nsystem and demonstrate numerically that it accurately reproduces the observed\nkink dynamics. Fourth, we report on a novel occurrence of length scale\ncompetition in this system and show how it can be understood by means of linear\nstability analysis. Finally, we conclude by summarizing the general physical\nframework that arises from our study.",
"arxiv_id": "patt-sol/9401005",
"authors": [
"Angel Sanchez",
"A R Bishop",
"Francisco Dominguez-Adame"
],
"categories": [
"patt-sol",
"cond-mat",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.49.4603",
"title": "Kink stability, propagation, and length scale competition in the periodically modulated sine-Gordon equation",
"url": "https://arxiv.org/abs/patt-sol/9401005"
},
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