Discrete Dynamics in Nature and Society 
Volume 2004 (2004), Issue 1, Pages 113-153
doi:10.1155/S1026022604311027

Generalized fermionic discrete Toda hierarchy

V. V. Gribanov,1 V. G. Kadyshevsky,2 and A. S. Sorin3

 1Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, Moscow Region, Dubna 141980, Russia
2Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Moscow Region, Dubna 141980, Russia
3Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Moscow Region, Dubna 141980, Russia
Received 16 November 2003

Abstract

We describe bi-Hamiltonian structure and Lax-pair formulation with the spectral parameter of the generalized fermionic Toda lattice hierarchy as well as its bosonic and fermionic symmetries for different (including periodic) boundary conditions. Its two reductions—N=4 and N=2 supersymmetric Toda lattice hierarchies—in different (including canonical) bases are investigated. Its r-matrix description, monodromy matrix, and spectral curves are discussed.