Hankel Determinant Approach to Generalized Vorob'ev-Yablonski Polynomials and Their Roots

Ferenc Balogh, Marco Bertola, Thomas Bothner*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Generalized Vorob’ev–Yablonski polynomials have been introduced by Clarkson and Mansfield in their study of rational solutions of the second Painlevé 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 a
partial characterization for the boundary curves of the highly regular patterns observed numerically in Clarkson and Mansfield (Nonlinearity 16(3):R1–R26, 2003).
Original languageEnglish
Pages (from-to)417-453
Number of pages37
JournalConstructive Approximation
Volume44
Early online date10 Mar 2016
DOIs
Publication statusE-pub ahead of print - 10 Mar 2016

Keywords

  • Vorob’ev-Yablonski polynomials
  • Hankel determinant representation, KdV and Painlev´e II hierarchy
  • Schur functions

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