On the extended multi-component Toda hierarchy
Abstract
The extended flow equations of the multi-component Toda hierarchy are constructed. We give the Hirota bilinear equations and tau function of this new extended multi-component Toda hierarchy(EMTH). Because of logarithmic terms, some extended vertex operators are constructed in generalized Hirota bilinear equations which might be useful in topological field theory and Gromov-Witten theory. Meanwhile the Darboux transformation and bi-Hamiltonian structure of this hierarchy are given. From the Hamiltonian tau symmetry, we give another different tau function of this hierarchy with some unknown mysterious connections with the one defined from the point of wave functions.
Cite
@article{arxiv.1410.3657,
title = {On the extended multi-component Toda hierarchy},
author = {Chuanzhong Li and Jingsong He},
journal= {arXiv preprint arXiv:1410.3657},
year = {2014}
}
Comments
29 Pages, to appear in Mathematical Physics, Analysis and Geometry. arXiv admin note: substantial text overlap with arXiv:1403.0684