On nonlinear equations integrable in theta functions of nonprincipally polarized Abelian varieties

Details On nonlinear equations integrable in theta functions of nonprincipally polarized Abelian varieties On nonlinear equations integrable in theta functions of nonprincipally polarized Abelian varieties

2001-10-26

arxiv.org/abs/math/0110290v1

Mathematics

Algebraic Geometry

LaTeX, 14 pages

Scientific paper

The formula of expanding the Abel variety theta function restricted to Abel subvariety into theta functions of this subvariety is obtained. With the help of this formula the solution of differential equations with Jacobi theta functions, restricted on a nonprincipally polarized Abel subvariety and their translations are rewritten in terms of the theta functions of these subvarieties. This is exemplified by the CKP equations, the Bogoyavlenskij system, and the Toda $g_2^{(1)}$-chain.

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