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dc.contributor.author Atkinson, J.
dc.date.accessioned 2019-02-14T17:29:25Z
dc.date.available 2019-02-14T17:29:25Z
dc.date.issued 2011
dc.identifier.citation Singularities of Type-Q ABS Equations / J. Atkinson // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 10 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 35Q58
dc.identifier.other DOI:10.3842/SIGMA.2011.073
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147397
dc.description.abstract The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities. uk_UA
dc.description.sponsorship This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html. The author gratefully acknowledges helpful discussions with Nalini Joshi. The research was funded by Australian Research Council Discovery Grants DP 0985615 and DP 110104151. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Singularities of Type-Q ABS Equations uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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