Symmetry Reduction of Asymmetric Heavenly Equation and 2+1-Dimensional Bi-Hamiltonian System

Abstract

Asymmetric heavenly equation, presented in a two-component form, is known to be 3+1-dimensional bi-Hamiltonian system. We show that symmetry reduction of this equation yields a new two component 2+1-dimensional integrable bi-Hamiltonian system. We prove that this new 2+1-dimensional system admits bi-Hamiltonian structure, so that it is integrable according to Magri's theorem.