Turkish Journal of Physics
Abstract
The first heavenly equation of Plebanski in the two-component form is known to be a $3+1$-dimensional tri-Hamiltonian system. We show that a particular choice of symmetry reduction applied to the first heavenly equation yields a $2+1$-dimensional bi-Hamiltonian system. For this tri-dimensional system, we present Lagrangian, Hamiltonian, and recursion operators; point symmetries; and integrals of motions.
DOI
10.3906/fiz-1710-5
Keywords
First heavenly equation, symmetry reduction, recursion operator, bi-Hamiltonian, $2+1$-dimensional systems
First Page
183
Last Page
190
Recommended Citation
YAZICI, DEVRİM
(2018)
"Symmetry reduction of the first heavenly equation and $2+1$-dimensional bi-Hamiltonian system,"
Turkish Journal of Physics: Vol. 42:
No.
2, Article 10.
https://doi.org/10.3906/fiz-1710-5
Available at:
https://journals.tubitak.gov.tr/physics/vol42/iss2/10
