Authors: DEVRİM YAZICI
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.
Keywords: First heavenly equation, symmetry reduction, recursion operator, bi-Hamiltonian, $2+1$-dimensional systems
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