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. Gribanov1
, V.G. Kadyshevsky2
and A.S. Sorin2
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
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.