Symmetry reduction of the first heavenly equation and 2

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.