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

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2009-07-17

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Blaszak, Maciej
Guerses, Metin
Zheltukhın, Kostyantyn

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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 R-3 are considered in detail.

Subject Keywords

Chains of co-rank, Co-rank

URI

https://hdl.handle.net/11511/32738

Journal

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

DOI

https://doi.org/10.1088/1751-8113/42/28/285204

Collections

Department of Mathematics, Article

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Citation Formats

M. Blaszak, M. Guerses, and K. Zheltukhın, “Bi-presymplectic chains of co-rank 1 and related Liouville integrable systems,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, pp. 0–0, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32738.