English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper focuses on the construction of rational solutions for the $A_{2n}$Painlev\'e system, also called the Noumi-Yamada system, which are consideredthe higher order generalizations of PIV. In this even case, we introduce amethod to construct the rational solutions based on cyclic dressing chains ofSchr\"{o}dinger operators with potentials in the class of rational extensionsof the harmonic oscillator. Each potential in the chain can be indexed by asingle Maya diagram and expressed in terms of a Wronskian determinant whoseentries are Hermite polynomials. We introduce the notion of cyclic Mayadiagrams and we characterize them for any possible period, using the conceptsof genus and interlacing. The resulting classes of solutions can be expressedin terms of special polynomials that generalize the families of generalizedHermite, generalized Okamoto and Umemura polynomials, showing that they areparticular cases of a larger family.

Cyclic Maya diagrams and rational solutions of higher order Painlev\'e systems