Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of Topological Charge using Theta-functional Formulae

Details Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of Topological Charge using Theta-functional Formulae Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of Topological Charge using Theta-functional Formulae

2009-04-29

arxiv.org/abs/0904.4520v1

Physics

Mathematical Physics

Accepted for publication in Volume 266 No. 3, of Proceedings of the Steklov Institute of Mathematics, 10 pages

Scientific paper

In this paper, we introduce the so-called multiscale limit for spectral
curves, associated with real finite-gap Sine-Gordon solutions. This technique
allows to solve the old problem of calculating the density of topological
charge for real finite-gap Sine-Gordon solutions directly from the
$\theta$-functional formulas.

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