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


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Blaszak M., Guerses M., ZHELTUKHIN K.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, cilt.42, 2009 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 42 Konu: 28
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1088/1751-8113/42/28/285204
  • Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Özet

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.