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# P.G.Grinevich, S.P.Novikov

## Toplological charge of the finite-gap Sine-Gordon solutions

The finite-gap solutions of the Sine-Gordon equations were constructed
about 20 years ago. One of the main characteristic of these solutions
is the topological charge and it is natural to pose the problem of
calculating it in terms of the spectral data. A formula for the spectral
charge was suggested by Dubrovin and Novikov, but they proof was based on
an assupmtion about the divisor behaviour, which is correct only in a
neighbourhoood of degenerate curves. A proof for general data is presented.