Sato theory on the $q$-Toda hierarchy and its extension
Abstract
In this paper, we construct the Sato theory including the Hirota bilinear equations and tau function of a new -deformed Toda hierarchy(QTH). Meanwhile the Block type additional symmetry and bi-Hamiltonian structure of this hierarchy are given. From Hamiltonian tau symmetry, we give another definition of tau function of this hierarchy. Afterwards, we extend the -Toda hierarchy to an extended -Toda hierarchy(EQTH) which satisfy a generalized Hirota quadratic equation in terms of generalized vertex operators. The Hirota quadratic equation might have further application in Gromov-Witten theory. The corresponding Sato theory including multi-fold Darboux transformations of this extended hierarchy is also constructed. At last, we construct the multicomponent extension of the -Toda hierarchy and show the integrability including its bi-Hamiltonian structure, tau symmetry and conserved densities.
Keywords
Cite
@article{arxiv.1504.06125,
title = {Sato theory on the $q$-Toda hierarchy and its extension},
author = {Chuanzhong Li},
journal= {arXiv preprint arXiv:1504.06125},
year = {2016}
}
Comments
28 Pages. arXiv admin note: substantial text overlap with arXiv:1403.0684