The Hamiltonian structures of the two-dimensional Toda lattice and R-matrices
We construct the tri-Hamiltonian structure of the two-dimensional Toda hierarchy using the R-matrix theory.
math-ph↗
arXiv subjects
Guido Carlet
Publications and source records attributed to Guido Carlet.
Extended Toda Lattice
We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.
nlin.SI↗
The Extended Toda Hierarchy
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the $CP^1$ topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter with certain extension of the nonlinear Schrödinger hierarchy.
nlin.SI↗