The symmetry structure of the anti-self-dual Einstein hierarchy

Abstract

An important example of a multi-dimensional integrable system is the anti-self-dual Einstein equations. By studying the symmetries of these equations, a recursion operator is found and the associated hierarchy constructed. Owing to the properties of the recursion operator one may construct a hierarchy of symmetries and find the algebra generated by them. In addition, the Lax pair for this hierarchy is constructed.

13 pages, LaTeX

References in corpus (4)

• SDiff(2) Toda equation -- hierarchy, $\tau$ function, and symmetries
• Classification of Generalized Symmetries for the Vacuum Einstein Equations
• On Self-Dual Gravity I
• Self-Dual Yang-Mills and the Hamiltonian Structures of Integrable Systems

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