Publication: Variational operators, symplectic operators, and the cohomology of scalar evolution equations
dc.contributor.author | Fels, M. E. | |
dc.contributor.author | Yaşar, E. | |
dc.contributor.buuauthor | YAŞAR, EMRULLAH | |
dc.contributor.department | Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü. | |
dc.contributor.orcid | 0000-0003-4732-5753 | |
dc.contributor.researcherid | AAG-9947-2021 | |
dc.date.accessioned | 2024-07-12T07:59:24Z | |
dc.date.available | 2024-07-12T07:59:24Z | |
dc.date.issued | 2019-06-04 | |
dc.description.abstract | For 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.doi | 10.1080/14029251.2019.1640470 | |
dc.identifier.endpage | 649 | |
dc.identifier.issn | 1402-9251 | |
dc.identifier.issue | 4 | |
dc.identifier.startpage | 604 | |
dc.identifier.uri | https://doi.org/10.1080/14029251.2019.1640470 | |
dc.identifier.uri | https://www.atlantis-press.com/journals/jnmp/125950493 | |
dc.identifier.uri | https://hdl.handle.net/11452/43229 | |
dc.identifier.volume | 26 | |
dc.identifier.wos | 000474780100007 | |
dc.indexed.wos | WOS.SCI | |
dc.language.iso | en | |
dc.publisher | Springernature | |
dc.relation.journal | Journal of Nonlinear Mathematical Physics | |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi | |
dc.rights | info:eu-repo/semantics/closedAccess | |
dc.subject | Inverse problem | |
dc.subject | Calculus | |
dc.subject | Bicomplexes | |
dc.subject | Variational bicomplex | |
dc.subject | Cohomology | |
dc.subject | Scalar evolution equation | |
dc.subject | Symplectic operator | |
dc.subject | Hamiltonian evolution equation | |
dc.subject | Mathematics | |
dc.subject | Physics | |
dc.title | Variational operators, symplectic operators, and the cohomology of scalar evolution equations | |
dc.type | Article | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | a5ff66ef-0c87-4d77-a467-e3150f51624c | |
relation.isAuthorOfPublication.latestForDiscovery | a5ff66ef-0c87-4d77-a467-e3150f51624c |