Geodesic
Multiscale Limit for Finite-Gap Sine-Gordon Solutions and Calculation of Topological Charge Using Theta-Functional Formulae
Informatics and Automation, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 54-63

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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. 
@article{TRSPY_2009_266_a2,
     author = {P. G. Grinevich and K. V. Kaipa},
     title = {Multiscale {Limit} for {Finite-Gap} {Sine-Gordon} {Solutions} and {Calculation} of {Topological} {Charge} {Using} {Theta-Functional} {Formulae}},
     journal = {Informatics and Automation},
     pages = {54--63},
     publisher = {mathdoc},
     volume = {266},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_266_a2/}
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P. G. Grinevich; K. V. Kaipa. Multiscale Limit for Finite-Gap Sine-Gordon Solutions and Calculation of Topological Charge Using Theta-Functional Formulae. Informatics and Automation, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 54-63. http://geodesic.mathdoc.fr/item/TRSPY_2009_266_a2/