Symmetries, integrals and hierarchies of new (3+1)-dimensional bi-Hamiltonian systems of Monge-Ampere type

Abstract

We study point symmetries, the corresponding conserved densities and hierarchies of four new bi-Hamiltonian heavenly systems in 3 + 1 dimensions which we discovered recently. We exhibit an important role played by the inverse recursion operators in the description of the hierarchies. Their use is twofold, either to provide the correct bi-Hamiltonian representation or to generate nonlocal symmetry flows. Invariant solutions w.r.t. nonlocal symmetries will generate (anti-)self-dual gravitational metrics which do not admit Killing vectors which is a characteristic feature of K3 gravitational instanton. (C) 2019 Elsevier B.V. All rights reserved.