Hamiltonian Structures of Fermionic Two-Dimensional Toda Lattice Hierarchies

Toda Lattice Realization of Integrable Hierarchies

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudodifferential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld–Sokolov realization.

Innnite Dimensional Lie Groups and the Two-dimensional Toda Lattice

1 Darboux Transformations for Nonlocal Two – Dimensional Toda Lattice

The technique of Darboux transformation is applied to nonlocal partner of two–dimensional periodic A n−1 Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The solutio...

New non-Noetherian Symmetries and Multi-Hamiltonian Structures for the Toda Lattice

New symmetry transformations for the n-dimensional Toda lattice are presented. Their existence allows for the construction of several first order Lagrangian structures associated to them. The multi-Hamiltonian structures are derived from Lagrangians in detail. The set of symmetries generates a Lie algebra.

Fermionic Spectrum on General Dimensional Hyperdiamond Lattice

We have constructed general dimensional hyperdiamond lattices which are analogues of the three dimensional diamond lattice. Each site has the minimal number of bonds as possible in that dimension and the structure of the bond vectors is similar to that of the Clifford algebra. Furthermore, the spectrum zeros of the tight-binding hopping model on the hyperdiamond lattice are also investigated. T...