SOLUTIONS OF NONLINEAR EQUATIONS INTEGRABLE IN JACOBI THETA FUNCTIONS BY THE METHOD OF THE INVERSE PROBLEM, AND SYMMETRIES OF ALGEBRAIC CURVES

Abstract

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 Schr?dinger and Koretweg-de Vries equations, and the period matrices of some hyperelliptic curves are computed explicitly. Bibliography: 35 titles.