Solutions of Nonlinear Equations Integrable in Jacobi Theta Functions by the Method of the Inverse Problem, and Symmetries of Algebraic Curves

A new approach is given for extracting from general formulas of finite-zone integration solutions of genus g>=2 expressible in terms of one-dimensional theta functions. As an application general formulas fo the type of the Lamb Ansatz for genus g=3 are found for the sine-Gordon, nonlinear Schrödinger and Koretweg-de Vries equations, and the period matrices of some hyperelliptic curves are computed explicitly.

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