Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
We show that under certain technical assumptions any weakly nonlocal Hamiltonian structure compatible with a given nondegenerate weakly nonlocal symplectic structure J can be written as the Lie derivative of J −1 along a suitably chosen nonlocal vector field. Moreover, we present a new description f...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147362 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility / A. Sergyeyev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 32 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862660472442978304 |
|---|---|
| author | Sergyeyev, A. |
| author_facet | Sergyeyev, A. |
| citation_txt | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility / A. Sergyeyev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that under certain technical assumptions any weakly nonlocal Hamiltonian structure compatible with a given nondegenerate weakly nonlocal symplectic structure J can be written as the Lie derivative of J −1 along a suitably chosen nonlocal vector field. Moreover, we present a new description for local Hamiltonian structures of arbitrary order compatible with a given nondegenerate local Hamiltonian structure of zero or first order, including Hamiltonian operators of the Dubrovin-Novikov type.
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| first_indexed | 2025-12-02T10:58:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147362 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T10:58:13Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sergyeyev, A. 2019-02-14T14:43:38Z 2019-02-14T14:43:38Z 2007 Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility / A. Sergyeyev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 32 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 37K05 https://nasplib.isofts.kiev.ua/handle/123456789/147362 We show that under certain technical assumptions any weakly nonlocal Hamiltonian structure compatible with a given nondegenerate weakly nonlocal symplectic structure J can be written as the Lie derivative of J −1 along a suitably chosen nonlocal vector field. Moreover, we present a new description for local Hamiltonian structures of arbitrary order compatible with a given nondegenerate local Hamiltonian structure of zero or first order, including Hamiltonian operators of the Dubrovin-Novikov type. This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. I am sincerely grateful to Prof. M. B laszak and Drs. M. Marvan, E.V. Ferapontov, M.V. Pavlov and R.G. Smirnov for stimulating discussions. I am also pleased to thank the referees for useful suggestions.This research was supported in part by the Czech Grant Agency (GA CR) under grant No. 201/04/0538, by the Ministry of Education, Youth and Sports of the Czech Republic (MSMTCR) under grant MSM 4781305904 and by Silesian University in Opava under grant IGS 1/2004. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility Article published earlier |
| spellingShingle | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility Sergyeyev, A. |
| title | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility |
| title_full | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility |
| title_fullStr | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility |
| title_full_unstemmed | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility |
| title_short | Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility |
| title_sort | weakly nonlocal hamiltonian structures: lie derivative and compatibility |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147362 |
| work_keys_str_mv | AT sergyeyeva weaklynonlocalhamiltonianstructuresliederivativeandcompatibility |