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Hamiltonian structures of generalized Manin-Radul super-KdV and constrained super KP hierarchies. (English) Zbl 0952.37033
The authors construct the Hamiltonian structures of the generalized Manin-Radul super KP and constrained super-KP hierarchies using the method of gauge transformations. It is shown that up to a sign Poisson brackets defined by Lax operators of Inami-Kanno super KdV hierarchy and constrained super Kadomtsev-Petviashvili have the same form. A detailed construction of the associated Hamiltonian structures for Inami-Kanno super KdV hierarchies and constrained modified super Kadomtsev-Petviashvili hierarchy is carried out with the help of the reduced supersymmetric Gelfand-Dickey brackets.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
81T60 Supersymmetric field theories in quantum mechanics
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