Bi-presymplectic chains of co-rank 1 and related Liouville integrable systems
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, cilt.42, sa.28, 2009 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42 Sayı: 28
- Basım Tarihi: 2009
- Doi Numarası: 10.1088/1751-8113/42/28/285204
- Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
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.