Multi-component Toda lattice hierarchy
Abstract
We give a detailed account of the N -component Toda lattice hierarchy. This hierarchy is an extended version of the one introduced by Ueno and Takasaki. Our version contains N discrete variables rather than one. We start from the Lax formalism, deduce the bilinear relation for the wave functions from it and then, based on the latter, prove existence of the tau-function. We also show how the multi-component Toda lattice hierarchy is embedded into the universal hierarchy which is basically the multi-component KP hierarchy. At last, we show how the bilinear integral equation for the tau-function can be obtained using the free fermion technique. An example of exact solutions (a multi-component analogue of one-soliton solutions) is given.
Cite
@article{arxiv.2412.20122,
title = {Multi-component Toda lattice hierarchy},
author = {T. Takebe and A. Zabrodin},
journal= {arXiv preprint arXiv:2412.20122},
year = {2026}
}
Comments
68 pages, no figure; rev. 72 pages, no figure (introduction extended); 2nd rev. 72 pages (several references added, typos corrected)