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Recursion operators and bi-Hamiltonian structure of the general heavenly equation | | M. B. Sheftel
; A. A. Malykh
; D. Yazıcı
; | | Date: |
13 Oct 2015 | | Abstract: | We discover two additional Lax pairs and three nonlocal recursion operators
for symmetries of the general heavenly equation introduced by Doubrov and
Ferapontov. Converting the equation to a two-component form, we obtain
Lagrangian and Hamiltonian structures of the two-component general heavenly
system. We study all point symmetries of the two-component system and, using
the inverse Noether theorem in the Hamiltonian form, obtain all the integrals
of motion corresponding to each variational (Noether) symmetry. We discover
that all the recursion operators coincide in the two-component form. Applying
the recursion operator to the first Hamiltonian structure we obtain second
Hamiltonian structure. We prove the Jacobi identities for the second
Hamiltonian operator and compatibility of the two Hamiltonian structures. Thus,
we demonstrate that the general heavenly equation in the two-component form is
a bi-Hamiltonian system integrable in the sense of Magri. We demonstrate how to
obtain nonlocal Hamiltonian flows generated by local Hamiltonians by using
Hermitian conjugate recursion operator. | | Source: | arXiv, 1510.3666 | | Services: | Forum | Review | PDF | Favorites | |
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