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Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік
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Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
Інший ID:
2000 Mathematics Subject Classification: 37K10; 37K05
Посилання:
Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility / A. Sergyeyev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 32 назв. — англ.
Підтримка:
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.
Дата:
2007
Переглядів:
561
Завантажень:
238
Анотація:
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.
