On Stieltjes relations, Painlev\'e-IV hierarchy and complex monodromy
Mathematical Physics
2009-10-31 v1 Complex Variables
math.MP
Abstract
A generalisation of the Stieltjes relations for the Painlev\'e-IV transcendents and their higher analogues determined by the dressing chains is proposed. It is proven that if a rational function from a certain class satisfies these relations it must be a solution of some higher Painlev\'e-IV equation. The approach is based on the interpretation of the Stieltjes relations as local trivial monodromy conditions for certain Schr\"odinger equations in the complex domain. As a corollary a new class of the Schr\"odinger operators with trivial monodromy is constructed in terms of the Painlev\'e-IV transcendents.
Cite
@article{arxiv.math-ph/0012040,
title = {On Stieltjes relations, Painlev\'e-IV hierarchy and complex monodromy},
author = {A. P. Veselov},
journal= {arXiv preprint arXiv:math-ph/0012040},
year = {2009}
}
Comments
11 pages