Special Solutions of the Hamiltonian System on an Elliptic Curve

J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 4, Page 669--687.

Sasaki, Yoshikatsu
Special Solutions of the Hamiltonian System on an Elliptic Curve
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]


Abstract:
Special solutions of Hamiltonian systems defined on an elliptic curve are studied; those solutions are reduced to the ordinary differential equation of the first order. The first integral of the equation is given in terms of a ratio of elliptic theta functions. Two cases of degeneration of the elliptic curve are also investigated. The functions describing the first integrals are similar to those given as solutions of Bruschi-Calogero equation.

Mathematics Subject Classification (2000): Primary 58F05; Secondary 33E05, 34A20
Mathematical Reviews Number: MR1947487

Received: 2001-04-27