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Cyclic Maya diagrams and rational solutions of higher order Painlevé systems

Clarkson, Peter A., Gómez‐Ullate, David, Grandati, Yves, Milson, Robert (2020) Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Studies in Applied Mathematics, . ISSN 0022-2526. (doi:10.1111/sapm.12300) (KAR id:79688)

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https://doi.org/10.1111/sapm.12300

Abstract

This paper focuses on the construction of rational solutions for the A2n-Painleve system, also called the Noumi-Yamada system, which are considered the higher order generalizations of PIV. In this even case, we introduce a method to construct the rational solutions based on cyclic dressing chains of Schrodinger operators with potentials in the class of rational extensions of the harmonic oscillator. Each potential in the chain can be indexed by a single Maya diagram and expressed in terms of a Wronskian determinant whose entries are Hermite polynomials. We introduce the notion of cyclic Maya diagrams and we characterize them for any possible period, using the concepts of genus and interlacing. The resulting classes of solutions can be expressed in terms of special polynomials that generalize the families of generalized Hermite, generalized Okamoto and Umemura polynomials, showing that they are particular cases of a larger family.

Item Type: Article
DOI/Identification number: 10.1111/sapm.12300
Uncontrolled keywords: Painleve equations, Noumi-Yamada systems, rational solutions, Darboux dressing, chains, Maya diagrams, Wronskian determinants, Hermite polynomials
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter Clarkson
Date Deposited: 23 Jan 2020 09:46 UTC
Last Modified: 31 Jan 2020 13:19 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/79688 (The current URI for this page, for reference purposes)
Clarkson, Peter A.: https://orcid.org/0000-0002-8777-5284
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