Generalization of bi-Hamiltonian systems in (3+1) dimension, possessing partner symmetries


YAZICI D.

JOURNAL OF GEOMETRY AND PHYSICS, cilt.101, ss.11-18, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 101
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.geomphys.2015.07.004
  • Dergi Adı: JOURNAL OF GEOMETRY AND PHYSICS
  • Sayfa Sayıları: ss.11-18

Özet

We study bi-Hamiltonian structure of a general equation which possesses partner symmetries. The general form of such second-order PDEs with four independent variables was determined in the paper Sheftel and Malykh (2009) on a classification of second-order PDEs which have this property. We apply Dirac's theory of constraints to this general equation. We formulate the equation in a two-component form and present the Lax pair of Olver lbragimov Shabat type. Under some constraints imposed on constant coefficients of this equation, we obtain its bi-Hamiltonian structure. Therefore, by Magri's theorem it is a completely integrable bi-Hamiltonian system in (3 + 1) dimensions. We also showed that with suitable choices of constant coefficients the equation is reduced to the well known integrable bi-Hamiltonian systems in (3 + 1) dimension. (C) 2016 Published by Elsevier B.V.