We introduce two algebraic completely integrable analogues of the Mumford systems which we call hyperelliptic Prym systems, because every hyperelliptic Prym variety appears as a fiber of their momentum map. As an application we show that the general fiber of the momentum map of the periodic Volterra lattice ȧi = ai (ai-1 - ai+1), i = 1,⋯,n, an+1 = a1, is an affine part of a hyperelliptic Prym variety, obtained by removing n translates of the theta divisor, and we conclude that this integrable system is algebraic completely integrable.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics