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

Geodesic

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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

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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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@article{IM2_1986_26_3_a1,
     author = {M. V. Babich and A. I. Bobenko and V. B. Matveev},
     title = {Solutions of nonlinear equations integrable in {Jacobi} theta functions by the method of the inverse problem, and symmetries of algebraic curves},
     journal = {Izvestiya. Mathematics },
     pages = {479--496},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a1/}
}

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M. V. Babich; A. I. Bobenko; V. B. Matveev. Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves. Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 479-496. http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a1/