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The paper develops an algebrotopological approach to the problem of effective selection of real finite-zone solutions of the sine-Gordon equation, which uses the socalledγ-representation on the Riemann surface, in which “action” variables can be computed explicitly. This approach is general and applies to many systems for which the reality problem has not yet been solved.

Algebrotopological approach to the reality problem. Real action variables in the theory of finite-zone solutions of the sine-Gordon equation