Publication:
Variational operators, symplectic operators, and the cohomology of scalar evolution equations

dc.contributor.authorFels, M. E.
dc.contributor.authorYaşar, E.
dc.contributor.buuauthorYAŞAR, EMRULLAH
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.
dc.contributor.orcid0000-0003-4732-5753
dc.contributor.researcheridAAG-9947-2021
dc.date.accessioned2024-07-12T07:59:24Z
dc.date.available2024-07-12T07:59:24Z
dc.date.issued2019-06-04
dc.description.abstractFor a scalar evolution equation u(t) = K(t, x, u, u(x), . . . , u(2m+1)) with m >= 1, the cohomology space H-1,H-2() is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for u(t) = K for which the equation is Hamiltonian is also shown to be isomorphic to the space H-1,H-2() and subsequently can be naturally identified with the space of variational operators. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The variational operator (or symplectic) nature of the potential form of a bi-Hamiltonian evolution equation is also presented in order to generate examples of interest.
dc.identifier.doi10.1080/14029251.2019.1640470
dc.identifier.endpage649
dc.identifier.issn1402-9251
dc.identifier.issue4
dc.identifier.startpage604
dc.identifier.urihttps://doi.org/10.1080/14029251.2019.1640470
dc.identifier.urihttps://www.atlantis-press.com/journals/jnmp/125950493
dc.identifier.urihttps://hdl.handle.net/11452/43229
dc.identifier.volume26
dc.identifier.wos000474780100007
dc.indexed.wosWOS.SCI
dc.language.isoen
dc.publisherSpringernature
dc.relation.journalJournal of Nonlinear Mathematical Physics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectInverse problem
dc.subjectCalculus
dc.subjectBicomplexes
dc.subjectVariational bicomplex
dc.subjectCohomology
dc.subjectScalar evolution equation
dc.subjectSymplectic operator
dc.subjectHamiltonian evolution equation
dc.subjectMathematics
dc.subjectPhysics
dc.titleVariational operators, symplectic operators, and the cohomology of scalar evolution equations
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublicationa5ff66ef-0c87-4d77-a467-e3150f51624c
relation.isAuthorOfPublication.latestForDiscoverya5ff66ef-0c87-4d77-a467-e3150f51624c

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