BI-HAMILTONIAN REPRESENTATION, SYMMETRIES AND INTEGRALS OF MIXED HEAVENLY AND HUSAIN SYSTEMS

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Sheftel M. B., YAZICI D.

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, cilt.17, sa.4, ss.453-484, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1142/s1402925110001021
  • Dergi Adı: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.453-484
  • Anahtar Kelimeler: Symmetries, integrals, Noether theorem, Lax pair, symplectic two-form, bi-Hamiltonian representation, PARTNER SYMMETRIES, EQUATIONS, MODEL
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation and Husain equation appear as closely related canonical equations admitting partner symmetries. Here for the mixed heavenly equation and Husain equation, formulated in a two-component form, we present recursion operators, Lax pairs of Olver-Ibragimov-Shabat type and discover their Lagrangians, symplectic and bi-Hamiltonian structure. We obtain all point and second-order symmetries, integrals and bi-Hamiltonian representations of these systems and their symmetry flows together with infinite hierarchies of nonlocal higher symmetries.