Bi-Hamiltonian structure of an asymmetric heavenly equation


Yazici D.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.44, no.50, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 50
  • Publication Date: 2011
  • Doi Number: 10.1088/1751-8113/44/50/505203
  • Title of Journal : JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Abstract

In the paper of Sheftel and Malykh (2009 J. Phys. A: Math. Theor. 42 395202) on the classification of second-order PDEs with four independent variables that possess partner symmetries, an asymmetric heavenly equation appears as one of the canonical equations admitting partner symmetries. Here, for the asymmetric heavenly equation formulated in a two-component form, we present the Lax pair of Olver-Ibragimov-Shabat type and obtain its multi-Hamiltonian structure. Therefore, by Magri's theorem, it is a completely integrable bi-Hamiltonian system in four dimensions.