English

A remark on the Hankel determinant formula for solutions of the Toda equation

Exactly Solvable and Integrable Systems 2009-11-13 v1

Abstract

We consider the Hankel determinant formula of the τ\tau functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the τ\tau functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.

Keywords

Cite

@article{arxiv.nlin/0701029,
  title  = {A remark on the Hankel determinant formula for solutions of the Toda equation},
  author = {Kenji Kajiwara and Marta Mazzocco and Yasuhiro Ohta},
  journal= {arXiv preprint arXiv:nlin/0701029},
  year   = {2009}
}

Comments

14 pages, IOP style