Integrable chains on algebraic curves
Abstract
The discrete Lax operators with the spectral parameter on an algebraic curve are defined. A hierarchy of commuting flows on the space of such operators is constructed. It is shown that these flows are linearized by the spectral transform and can be explicitly solved in terms of the thetafunctions of the spectral curves. The Hamiltonian theory of the corresponding systems is analyzed. The new type of completely integrable Hamiltonian systems associated with the space of rank $r=2$ discrete Lax operators on a {\it variable} base curve is found.
 Publication:

arXiv eprints
 Pub Date:
 September 2003
 DOI:
 10.48550/arXiv.hepth/0309255
 arXiv:
 arXiv:hepth/0309255
 Bibcode:
 2003hep.th....9255K
 Keywords:

 High Energy Physics  Theory;
 Algebraic Geometry
 EPrint:
 19 pages, Latex