Topological charge of the real periodic finite-gap Sine-Gordon solutionsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 9 июня 2015 г.
Аннотация:An effective description of the inverse spectral data corresponding to the real periodic and quasi-periodic finite-gap (algebro-geometrical) solutions for the sine-Gordon equation is obtained. In particular, the explicit formula for the so-called topological charge of the solutions is found and proven. As was already understood 20 years ago, it is very hard to extract any formula for this quantity from the Θ-functional expressions. A new method was developed by the authors for this goal. In Appendix C an analogue of the Fourier-Laurent integral transform on the Riemann surface is defined, based on the constructions of soliton theory. It is a natural continuous analogue of the discrete Krichever-Novikov bases developed in the late 1980s for the needs of the operator quantization of string theory.