Integrable systems, poisson pencils, and hyperelliptic lax pairs

A new Lax pair for the multidimensional Manakov system on the Lie algebra so(m) with a spectral parameter defined on a certain unramified covering of a hyperelliptic curve is considered. For the Clebsh-Perelomov system on the Lie algebra e(n), similar pairs are presented. Multidimensional analogs of the classical integrable Steklov-Lyapunov system describing a motion of a rigid body in an ideal fluid are found. Bibliography: 15 titles. © 1999 Kluwer Academic/Plenum Publishers.