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Cyclic Maya diagrams and rational solutions of higher order Painlevé systems

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dc.contributor.authorGómez Ullate, David
dc.contributor.authorClarkson, Peter
dc.contributor.authorGrandati, Yves
dc.contributor.authorMilson, Robert
dc.contributor.rorhttps://ror.org/02jjdwm75
dc.date.accessioned2025-02-18T11:59:35Z
dc.date.available2025-02-18T11:59:35Z
dc.date.issued2020-01-22
dc.description.abstractThis paper focuses on the construction of rational solutions for the A2n-Painlev´e 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 Schr¨odinger 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.
dc.description.peerreviewedyes
dc.description.statusPublished
dc.formatapplication/pdf
dc.identifier.citationClarkson, P. A., Gómez‐Ullate, D., Grandati, Y., & Milson, R. (2020). Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Studies in Applied Mathematics, 144(3), 357-385. https://doi.org/10.48550/arXiv.1811.09274
dc.identifier.doi https://doi.org/10.1111/sapm.12300
dc.identifier.issn1467-9590
dc.identifier.urihttps://hdl.handle.net/20.500.14417/3563
dc.issue.number3
dc.journal.titleStudies in Applied Mathematics
dc.language.isoen
dc.page.total26
dc.publisherWiley
dc.relation.departmentApplied Mathematics
dc.relation.entityIE University
dc.relation.schoolIE School of Science & Technology
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.en
dc.subject.keywordPainlev´e equations
dc.subject.keywordNoumi-Yamada systems
dc.subject.keywordRational solutions
dc.subject.keywordDarboux dressing chains
dc.subject.keywordMaya diagrams
dc.subject.keywordWronskian determinants
dc.subject.keywordHermite polynomials
dc.titleCyclic Maya diagrams and rational solutions of higher order Painlevé systems
dc.typeinfo:eu-repo/semantics/article
dc.version.typeinfo:eu-repo/semantics/acceptedVersion
dc.volume.number144
dspace.entity.typePublication
relation.isAuthorOfPublicationd0525f43-b84b-4613-9984-4324ddf81556
relation.isAuthorOfPublication.latestForDiscoveryd0525f43-b84b-4613-9984-4324ddf81556
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