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, vol.17, no.4, pp.453-484, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.1142/s1402925110001021
  • Title of Journal : JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
  • Page Numbers: pp.453-484
  • Keywords: Symmetries, integrals, Noether theorem, Lax pair, symplectic two-form, bi-Hamiltonian representation, PARTNER SYMMETRIES, EQUATIONS, MODEL

Abstract

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.