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Article overview
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Multi-Hamiltonian structure of self-dual gravity | | M. B. Sheftel
; D. Yazici
; | | Date: |
17 Feb 2008 | | Abstract: | We discover multi-Hamiltonian structure of the complex Monge-Ampere equation
(CMA) set in a real first-order two-component form. Therefore, by Magri’s
theorem this is a completely integrable system in four real dimensions. We
start with Lagrangian and Hamiltonian densities in real variables, a symplectic
form and the Hamiltonian operator, that determines the Poisson bracket. We have
calculated all point symmetries of the two-component CMA system and
Hamiltonians of the symmetry flows. We have found two new real recursion
operators for symmetries which commute with the operator of a symmetry
condition on solutions of the CMA system. These two couples of operators form
two Lax pairs for the two-component system. The recursion operators, being
applied to the first Hamiltonian operator, generate infinitely many real
Hamiltonian structures. We show how to construct an infinite hierarchy of
higher commuting flows together with the corresponding infinite chain of their
Hamiltonians. | | Source: | arXiv, 0802.2203 | | Services: | Forum | Review | PDF | Favorites | |
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