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dc.contributor.authorDragović, Vladimiren_US
dc.contributor.authorGontsov, Renaten_US
dc.contributor.authorShramchenko, Vasilisaen_US
dc.date.accessioned2021-07-14T10:54:01Z-
dc.date.available2021-07-14T10:54:01Z-
dc.date.issued2021-10-01-
dc.identifier.issn0167-2789-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/4616-
dc.description.abstractWe study the Schlesinger system of partial differential equations in the case when the unknown matrices of arbitrary size (p×p) are triangular and the eigenvalues of each matrix form an arithmetic progression with a rational difference q, the same for all matrices. We show that such a system possesses a family of solutions expressed via periods of meromorphic differentials on the Riemann surfaces of superelliptic curves. We determine the values of the difference q, for which our solutions lead to explicit polynomial or rational solutions of the Schlesinger system. As an application of the (2×2)-case, we obtain explicit sequences of rational solutions and of one-parameter families of rational solutions of Painlevé VI equations. Using similar methods, we provide algebraic solutions of particular Garnier systems.en_US
dc.publisherElsevieren_US
dc.relation.ispartofPhysica D: Nonlinear Phenomenaen_US
dc.subjectGarnier systems | Painlevé VI equations | Periods of differentials | Rational solutions | Superelliptic curves | Triangular Schlesinger systemsen_US
dc.titleTriangular Schlesinger systems and superelliptic curvesen_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.physd.2021.132947-
dc.identifier.scopus2-s2.0-85106879616-
dc.contributor.affiliationMechanicsen_US
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage132947-
dc.relation.volume424-
dc.description.rank~M21-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0002-0295-4743-
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