- Turkish Journal of Physics
- Vol: 42 Issue: 2
- Symmetry reduction of the rst heavenly equation and 2 + 1 -dimensional bi-Hamiltonian system
Symmetry reduction of the rst heavenly equation and 2 + 1 -dimensional bi-Hamiltonian system
Authors : Devrim Yazici
Pages : 183-190
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :The first heavenly equation of Plebanski in the two-component form is known to be a 3 + 1 " role="presentation"> 3 + 1 3 + 1 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 " role="presentation"> 2 + 1 2 + 1 2+1 -dimensional bi-Hamiltonian system. For this tri-dimensional system, we present Lagrangian, Hamiltonian, and recursion operators; point symmetries; and integrals of motions.Keywords : First heavenly equation, symmetry reduction, recursion operator, bi-Hamiltonian, 2 + 1-dimensional systems