On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems

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dc.contributor.authorPrykarpatski, A.K.
dc.date.accessioned2025-11-21T18:54:41Z
dc.date.issued2018
dc.description.abstractIn this letter, I analyze a covering jet manifold scheme, its relation to the invariant theory of the associated vector fields, and applications to the Lax-Sato-type integrability of nonlinear dispersionless differential systems. The related contact geometry linearization covering scheme is also discussed. The devised techniques are demonstrated for such nonlinear Lax-Sato integrable equations as Gibbons-Tsarev, ABC, Manakov-Santini, and the differential Toda singular manifold equations.
dc.description.sponsorshipThe author cordially thanks Professors M. Blaszak, B. Szablikowski, and J. Cieślinski for useful discussions of the results during the International Conference in Functional Analysis dedicated to the 125th anniversary of Stefan Banach held on 18–23 September 2017 in Lviv, Ukraine. He is also greatly indebted to Professors V.E. Zakharov (University of Arizona, Tucson) and J. Szmigelski University of Saskatchewan, Saskatoon) for their interest in the work and instructive discussions during the XXXV Workshop on Geometric Methods in Physics, held in Białowieża, Poland. The author is grateful to Professor B. Kruglikov (University of Tromsø, Norway) for his interest in the work and for mentioning some misprints and important references, which were very helpful in preparing the manuscript. He is also indebted to the referees for their remarks and instrumental suggestions. Last but not least, thanks go to the Department of Mathematical Sciences of NJIT (Newark, NJ, USA) for the invitation to visit NJIT during the Summer Semester of 2017, where an essential part of this paper was completed. Local support from the Institute of Mathematics at the Kraków University of Technology is also much appreciated.
dc.identifier.citationOn the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems / A.K. Prykarpatski // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2018.023
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 17B68; 17B80; 35Q53; 35G25; 35N10; 37K35; 58J70; 58J72; 34A34; 37K05; 37K10
dc.identifier.otherarXiv: 1801.07312
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/209441
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleOn the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2018, том 14, випуск за цей рік