Multiscale Limit for Finite-Gap Sine-Gordon Solutions and Calculation of Topological Charge Using Theta-Functional Formulae

P. G. Grinevich^a, K. V. Kaipa<sup>b

a</sup> Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, Russia
^b Department of Mathematics, University of Maryland, College Park, MD, USA

Abstract: We introduce the so-called multiscale limit for spectral curves associated with real finite-gap sine-Gordon solutions. This technique allows us to solve the old problem of calculating the density of the topological charge for real finite-gap sine-Gordon solutions directly from the $\theta$-functional formulae.

UDC: 517.958

Received in April 2009

 English version: Proceedings of the Steklov Institute of Mathematics, 2009, 266, 49–58

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