Proceedings of the International Conference on Geometry, Integrability and Quantization

Symmetry Reduction of Asymmetric Heavenly Equation and 2+1-Dimensional Bi-Hamiltonian System

Devrim Yazıcı and Hakan Sert

Abstract

Asymmetric heavenly equation, presented in a two-component form, is known to be 3+1-dimensional bi-Hamiltonian system. We show that symmetry reduction of this equation yields a new two component 2+1-dimensional integrable bi-Hamiltonian system. We prove that this new 2+1-dimensional system admits bi-Hamiltonian structure, so that it is integrable according to Magri's theorem.

Article information

Source
Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2014), 309-317

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815719

Digital Object Identifier
doi:10.7546/giq-15-2014-309-317

Mathematical Reviews number (MathSciNet)
MR3287766

Zentralblatt MATH identifier
1330.37053

Citation

Yazıcı, Devrim; Sert, Hakan. Symmetry Reduction of Asymmetric Heavenly Equation and 2+1-Dimensional Bi-Hamiltonian System. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 309--317, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-309-317. https://projecteuclid.org/euclid.pgiq/1436815719


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