On an integrable multi-dimensionally consistent 2n+2n-dimensional heavenly-type equation
Exactly Solvable and Integrable Systems
2019-02-19 v1 Mathematical Physics
math.MP
Abstract
Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2n+2n-dimensional integrable partial differential equation with the associated eigenfunction constituting an infinitesimal symmetry. The "universal" character of this novel equation of vanishing Pfaffian type is demonstrated by retrieving and generalising to higher dimensions a great variety of well-known integrable equations such as the dispersionless KP and Hirota equations and various avatars of the heavenly equation governing self-dual Einstein spaces.
Cite
@article{arxiv.1902.06045,
title = {On an integrable multi-dimensionally consistent 2n+2n-dimensional heavenly-type equation},
author = {B. G. Konopelchenko and W. K. Schief},
journal= {arXiv preprint arXiv:1902.06045},
year = {2019}
}