Publication: Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation
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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 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 that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that 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 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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© 1994 The American Physical Society.
We are indebted to Rainer Scharf, David Cai, and Maxi San Miguel for enlightening conversations on this research. A.S. is supported by the Ministerio de Educacion y Ciencia (Spain) and the Fulbright Fund, by Direccion General de Investigacion Cientifica y Tecnica (Spain) through Project No. PB92-0378, and by the European Union (¹tmork on Nonlinear Spatio-Temporal Structures in Semiconductor, Fluids, and Oscillator Ensembles). He also thanks the Los Alamos National Laboratory for warm hospitality and a productive atmosphere. Work at Los Alamos is performed under the auspices of the U.S. Department of Energy.
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