Hankel Determinant Approach to Generalized Vorob'ev-Yablonski Polynomials and their Roots
Mathematical Physics
2015-04-03 v1 Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
Generalized Vorob'ev-Yablonski polynomials have been introduced by Clarkson and Mansfield in their study of rational solutions of the second Painlev\'e hierarchy. We present new Hankel determinant identities for the squares of these special polynomials in terms of Schur polynomials. As an application of the identities, we analyze the roots of generalized Vorob'ev-Yablonski polynomials and provide formul\ae\, for the boundary curves of the highly regular patterns observed numerically in \cite{CM}.
Keywords
Cite
@article{arxiv.1504.00440,
title = {Hankel Determinant Approach to Generalized Vorob'ev-Yablonski Polynomials and their Roots},
author = {Ferenc Balogh and Marco Bertola and Thomas Bothner},
journal= {arXiv preprint arXiv:1504.00440},
year = {2015}
}
Comments
23 pages, 10 figures