2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228887In 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 $θ$-functional formulas.Accepted for publication in Volume 266 No. 3, of Proceedings of the Steklov Institute of Mathematics, 10 pagesMathematical Physicstext