On the Classification of Fifth Order Quasi-Linear Non-Constant Separant Scalar Evolution Equations of the Kdv-Type

dc.contributor.authorÖzkum, Gülcan
dc.contributor.authorBilge, Ayşe Hümeyra
dc.date.accessioned2021-02-07T16:24:07Z
dc.date.available2021-02-07T16:24:07Z
dc.date.issued2012
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.description.abstractFifth order, quasi-linear, non-constant separant evolution equations are of the form u(t) = A(partial derivative(5)u/partial derivative x(5)) + (B) over tilde, where A and (B) over tilde are functions of x, t, u and of the derivatives of u with respect to x up to order 4. We use the existence of a "formal symmetry'', hence the existence of "canonical conservation laws'' rho((i)), i = -1, . . . , 5 as an integrability test. We define an evolution equation to be of the KdV-Type, if all odd numbered canonical conserved densities are nontrivial. We prove that fifth order, quasi-linear, non-constant separant evolution equations of KdV type are polynomial in the function a = A(1/5); a = (alpha u(3)(2) + beta u(3) + gamma)(-1/2), where alpha, beta, and gamma are functions of x, t, u and of the derivatives of u with respect to x up to order 2. We determine the u(2) dependency of a in terms of P = 4 alpha gamma - beta(2) > 0 and we give an explicit solution, showing that there are integrable fifth order non-polynomial evolution equations.en_US
dc.description.sponsorshipTubitaken_US
dc.identifier.citation2
dc.identifier.doi10.1143/JPSJ.81.054001en_US
dc.identifier.issn0031-9015en_US
dc.identifier.issn0031-9015
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-84860627338en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12469/3880
dc.identifier.urihttps://doi.org/10.1143/JPSJ.81.054001
dc.identifier.volume81en_US
dc.identifier.wosWOS:000303244800005en_US
dc.institutionauthorBilge, Ayşe Hümeyraen_US
dc.institutionauthorBilge, Ayşe Hümeyra
dc.language.isoenen_US
dc.publisherPhysical Soc Japanen_US
dc.relation.journalJournal of the Physical Society of Japanen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectEvolution equationsen_US
dc.subjectIntegrabilityen_US
dc.subjectClassificationen_US
dc.subjectRecursion operatoren_US
dc.subjectFormal symmetryen_US
dc.titleOn the Classification of Fifth Order Quasi-Linear Non-Constant Separant Scalar Evolution Equations of the Kdv-Typeen_US
dc.typeArticleen_US
dspace.entity.typePublication
relation.isAuthorOfPublication1b50a6b2-7290-44da-b8d5-f048fea8b315
relation.isAuthorOfPublication.latestForDiscovery1b50a6b2-7290-44da-b8d5-f048fea8b315

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