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On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators

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dc.contributor.author Talati, D.
dc.contributor.author Turhan, R.
dc.date.accessioned 2019-02-14T17:52:37Z
dc.date.available 2019-02-14T17:52:37Z
dc.date.issued 2011
dc.identifier.citation On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators / D. Talati, R. Turhan // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 37K05; 37K10
dc.identifier.other DOI: http://dx.doi.org/10.3842/SIGMA.2011.081
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147408
dc.description.abstract We show that a recently introduced fifth-order bi-Hamiltonian equation with a differentially constrained arbitrary function by A. de Sole, V.G. Kac and M. Wakimoto is not a new one but a higher symmetry of a third-order equation. We give an exhaustive list of cases of the arbitrary function in this equation, in each of which the associated equation is inequivalent to the equations in the remaining cases. The equations in each of the cases are linked to equations known in the literature by invertible transformations. It is shown that the new Hamiltonian operator of order seven, using which the introduced equation is obtained, is trivially related to a known pair of fifth-order and third-order compatible Hamiltonian operators. Using the so-called trivial compositions of lower-order Hamiltonian operators, we give nonlocal generalizations of some higher-order Hamiltonian operators. uk_UA
dc.description.sponsorship R.T. thanks Professors M. G¨urses and A. Karasu for stimulating discussions; and Professor V.G. Kac for comments and clarification of the parametric nature of their results, removing a misinterpretation with incorrect consequences. D.T. is supported by TUB¨ ˙ITAK PhD Fellowship for Foreign Citizens. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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