Bi-Hamiltonian structure of an asymmetric heavenly equation
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.44, no.50, 2011 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 44 Issue: 50
- Publication Date: 2011
- Doi Number: 10.1088/1751-8113/44/50/505203
- Journal Name: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Yıldız Technical University Affiliated: Yes
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.