On an integrable multi-dimensionally consistent 2 n + 2 n -dimensional heavenly-type equation

Abstract

Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2 n  + 2 n -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 generalizing to higher dimensions a great variety of well-known integrable equations such as the dispersionless Kadomtsev–Petviashvili and Hirota equations and various avatars of the heavenly equation governing self-dual Einstein spaces.