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Perturbation theory for localized solutions of sine-Gordon equation: decay of a breather and pinning by 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 influence of inhomogeneities are taken into account as perturbations to exact solutions of the sine-Gordon equation. We have investigated two special cases of fluxon trapped by a microresistor and decay of a breather under dissipation. Also, we have carried out numerical simulations with dissipative sine-Gordon equation and made comparison with the McLaughlin-Scott theory. Significant distinction between the McLaughlin-Scott calculation for a breather decay and our numerical result indicates that the history dependence of the breather evolution can not be neglected even for small damping parameter.

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D. R. Gulevich, F. V. Kusmartsev. 2006-08-11. Perturbation theory for localized solutions of sine-Gordon equation: decay of a breather and pinning by microresistor. https://doi.org/10.1103/physrevb.74.214303

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