Perturbation theory for localized solutions of the sine-Gordon equation: Decay of a breather and pinning by a microresistor

D. R. Gulevich, F. V. Kusmartsev

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Abstract

We develop a perturbation theory that describes bound states of solitons localized in a confined area. External forces and the influence of inhomogeneities are taken into account as perturbations to exact solutions of the sine-Gordon equation. We have investigated two special cases: a fluxon trapped by a microresistor and decay of a breather under dissipation. We have also carried out numerical simulations with the dissipative sine-Gordon equation and made a comparison with the McLaughlin-Scott theory. A significant distinction between the McLaughlin-Scott calculation for a breather decay and our numerical result indicates that the history dependence of the breather evolution cannot be neglected even for a small damping parameter.

Original languageBritish English
Article number214303
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume74
Issue number21
DOIs
StatePublished - 2006

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