Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves

M. V. Babich ; A. I. Bobenko ; V. B. Matveev

Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 479-496.

Résumé

A new approach is given for extracting from general formulas of finite-zone integration solutions of genus $g\geqslant2$ 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. Bibliography: 35 titles.

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