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Separation of variables for some systems with a fourth-order integral of motion
Authors:Yu. A. Grigoryev  V. A. Khudobakhshov  A. V. Tsiganov
Affiliation:1. St. Petersburg State University, St. Petersburg, Russia
Abstract:We construct separation variables for Yehia’s integrable deformations of the Kovalevskaya top and the Chaplygin system on a sphere. In the general case, the corresponding quadratures are given by the Abel-Jacobi map on a two-dimensional submanifold of the Jacobian of a genus-three algebraic curve, which is not hyperelliptic.
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