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

Abstract

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.

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