Physics – Mathematical Physics
Scientific paper
2001-11-20
Physics
Mathematical Physics
30 Pages, 4 Fig, Latex
Scientific paper
An effective description of the inverse spectral data corresponding to the real periodic and quasiperiodic 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 proved. As it was understood already 20 years ago, it is very hard to extract any formula for this quantity from the Theta-functional expressions. A new method was developed by the authors for this goal. In the appendix 3 an analog of the Fourier-Laurent integral transform on the Riemann surfaces is defined, based on the constructions of the Soliton Theory. It is a natural continuous analog of the discrete Krichever-Novikov bases developed in the late 80s for the needs of the Operator Quantization of String Theory.
Grinevich Petr G.
Novikov Sergey P.
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