On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147408 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862745814340730880 |
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| author | Talati, D. Turhan, R. |
| author_facet | Talati, D. Turhan, R. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T20:42:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147408 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:42:35Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Talati, D. Turhan, R. 2019-02-14T17:52:37Z 2019-02-14T17:52:37Z 2011 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. 1815-0659 2010 Mathematics Subject Classification: 37K05; 37K10 DOI: http://dx.doi.org/10.3842/SIGMA.2011.081 https://nasplib.isofts.kiev.ua/handle/123456789/147408 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators Article published earlier |
| spellingShingle | On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators Talati, D. Turhan, R. |
| title | On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators |
| title_full | On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators |
| title_fullStr | On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators |
| title_full_unstemmed | On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators |
| title_short | On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators |
| title_sort | on a recently introduced fifth-order bi-hamiltonian equation and trivially related hamiltonian operators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147408 |
| work_keys_str_mv | AT talatid onarecentlyintroducedfifthorderbihamiltonianequationandtriviallyrelatedhamiltonianoperators AT turhanr onarecentlyintroducedfifthorderbihamiltonianequationandtriviallyrelatedhamiltonianoperators |