Symmetry reduction of asymmetric heavenly equation and \(2+1\)-dimensional bi-Hamiltonian system. (English) Zbl 1300.35126

Yazici, Devrim; Sert, Hakan

J. Geom. Symmetry Phys. 34, 87-96 (2014).

Summary: 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.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
70F15	Celestial mechanics
83C05	Einstein’s equations (general structure, canonical formalism, Cauchy problems)