Bi-Hamiltonian structures for integrable systems on regular time scales

Szablikowski B. M., Blaszak M., Silindir B.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.50, sa.7, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 7
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1063/1.3158860
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: functional analysis, Poisson equation, recursive functions, tensors, OPERATORS, ALGEBRA
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of delta-pseudodifferential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors are given by the use of the recursion operators of the Lax hierarchies. The theory is illustrated by Delta-differential counterparts of Ablowitz-Kaup-Newell-Segur and Kaup-Broer hierarchies.