Multi-Hamiltonian structure of Plebanski's second heavenly equation
Exactly Solvable and Integrable Systems
2009-11-11 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
Differential Geometry
math.MP
Abstract
We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.
Keywords
Cite
@article{arxiv.nlin/0505030,
title = {Multi-Hamiltonian structure of Plebanski's second heavenly equation},
author = {F. Neyzi and Y. Nutku and M. B. Sheftel},
journal= {arXiv preprint arXiv:nlin/0505030},
year = {2009}
}