Bi-presymplectic chains of co-rank 1 and related Liouville integrable systems

Bi-presymplectic chains of 1-forms of co-rank 1 are considered. The conditions under which such chains represent some Liouville integrable systems and the conditions under which there exist related bi-Hamiltonian chains of vector fields are derived. To present the construction of bi-presymplectic ch...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2009-07, Vol.42 (28), p.285204-285204 (19)
Main Authors: Błaszak, Maciej, Gürses, Metin, Zheltukhin, Kostyantyn
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:Bi-presymplectic chains of 1-forms of co-rank 1 are considered. The conditions under which such chains represent some Liouville integrable systems and the conditions under which there exist related bi-Hamiltonian chains of vector fields are derived. To present the construction of bi-presymplectic chains, the notion of a dual Poisson-presymplectic pair is used, and the concept of d-compatibility of Poisson bivectors and d-compatibility of presymplectic forms is introduced. It is shown that bi-presymplectic representation of a related flow leads directly to the construction of separation coordinates in a purely algorithmic way. As an illustration, bi-presymplectic and bi-Hamiltonian chains in are considered in detail.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/28/285204