Abstract
We consider the “even-time” flow of the Manin-Radul supersymmetric KP hierarchy and show that they possess bi-hamiltonian structures by deriving two distinct Gelfand-Dikii brackets corresponding to two successive hamiltonians of the system. A recursion relation involving them is also obtained. We observe that the first hamiltonian structure defines a supersymmetric Lie algebra since it is a linear algebra among the super fields appearing in the Lax operator whereas the second hamiltonian structure is a non-linear algebra and so it does not define a Lie algebra.
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