'Level grading' a new graded algebra structure on differential polynomials: application to the classification of scalar evolution equations

dc.contributor.authorBilge, Ayşe Hümeyra
dc.contributor.authorBilge, Ayşe Hümeyra
dc.date.accessioned2019-06-27T08:03:24Z
dc.date.available2019-06-27T08:03:24Z
dc.date.issued2013
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.description.abstractWe define a new grading which we call the 'level grading' on the algebra of polynomials generated by the derivatives u(k+i) over the ring K-(k) of C-infinity functions of x t u u(1) ... u(k) where . This grading has the property that the total derivative and the integration by parts with respect to x are filtered algebra maps. In addition if u satisfies the evolution equation u(j) = F[u] where F is a polynomial of order m = k + p and of level p then the total derivative with respect to t D-t is also a filtered algebra map. Furthermore if the separant partial derivative F/partial derivative u(m) belongs to K-(k) then the canonical densities (i) are polynomials of level 2i + 1 and (i) is of level 2i + 1 + m. We define 'KdV-like' evolution equations as those equations for which all the odd canonical densities rho((i)) are non-trivial. We use the properties of level grading to obtain a preliminary classification of scalar evolution equations of orders m = 7 9 11 13 up to their dependence on x t u u(1) and u(2). These equations have the property that the canonical density rho((-1)) is (alpha u(3)(2) + beta u(3) + gamma)(1/2) where alpha beta and gamma are functions of x t u u(1) u(2). This form of rho((-1)) is shared by the essentially nonlinear class of third order equations and a new class of fifth order equations.en_US]
dc.identifier.citation1
dc.identifier.doi10.1088/1751-8113/46/38/385202en_US
dc.identifier.issn1751-8113en_US
dc.identifier.issn1751-8113
dc.identifier.issue38
dc.identifier.scopus2-s2.0-84883852654en_US
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://hdl.handle.net/20.500.12469/785
dc.identifier.urihttps://doi.org/10.1088/1751-8113/46/38/385202
dc.identifier.volume46en_US
dc.identifier.wosWOS:000324073500005en_US
dc.identifier.wosqualityQ2
dc.institutionauthorBilge, Ayşe Hümeyraen_US
dc.language.isoenen_US
dc.publisherIOP Publishing Ltden_US
dc.relation.journalJournal Of Physics A-Mathematical And Theoreticalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.title'Level grading' a new graded algebra structure on differential polynomials: application to the classification of scalar evolution equationsen_US
dc.typeArticleen_US
dspace.entity.typePublication
relation.isAuthorOfPublication1b50a6b2-7290-44da-b8d5-f048fea8b315
relation.isAuthorOfPublication.latestForDiscovery1b50a6b2-7290-44da-b8d5-f048fea8b315

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