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Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations

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dc.contributor.authorSinelshchikov, D. I.
dc.contributor.authorGaiur, I. Y.
dc.contributor.authorKudryashov, N. A.
dc.contributor.authorКудряшов, Николай Алексеевич
dc.date.accessioned2024-11-21T11:15:00Z
dc.date.available2024-11-21T11:15:00Z
dc.date.issued2019
dc.description.abstract© 2019 Elsevier Inc.We consider a family of non-autonomous second-order differential equations, which generalizes the Liénard equation. We explicitly find the necessary and sufficient conditions for members of this family of equations to admit quadratic, with the respect to the first derivative, first integrals. We show that these conditions are equivalent to the conditions for equations in the family under consideration to possess Lax representations. This provides a connection between the existence of a quadratic first integral and a Lax representation for the studied dissipative differential equations, which may be considered as an analogue to the theorem that connects Lax integrability and Arnold–Liouville integrability of Hamiltonian systems. We illustrate our results by several examples of dissipative equations, including generalizations of the Van der Pol and Duffing equations, each of which have both a quadratic first integral and a Lax representation.
dc.identifier.citationSinelshchikov, D. I. Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations / Sinelshchikov, D.I., Gaiur, I.Y., Kudryashov, N.A. // Journal of Mathematical Analysis and Applications. - 2019. - 480. - № 1. - 10.1016/j.jmaa.2019.123375
dc.identifier.doi10.1016/j.jmaa.2019.123375
dc.identifier.urihttps://www.doi.org/10.1016/j.jmaa.2019.123375
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85070851027&origin=resultslist
dc.identifier.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000483414100014
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/18573
dc.relation.ispartofJournal of Mathematical Analysis and Applications
dc.titleLax representation and quadratic first integrals for a family of non-autonomous second-order differential equations
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue1
oaire.citation.volume480
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