Symmetry reduction of the first heavenly equation and $2+1$-dimensional bi-Hamiltonian system


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

Full Text: PDF