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Behaviors of \(N = 1\) supersymmetric Euler derivatives and Hamiltonian operators under general superconformal transformations. (English) Zbl 1317.37079

Summary: The changing rule of super Hamiltonian operators under general superconformal transformations is established by means of investigating behavior of supersymmetric Euler derivatives under the same kind of changes of variables. In the two particular yet frequent cases such as supersymmetric Miura-type transformations and reciprocal transformations, the results are detailed and applied to construct bi-Hamiltonian structures of some supersymmetric evolution equations. As an interesting example, one of supersymmetric Harry Dym equations is shown to be a bi-Hamiltonian system through its reciprocal link to the classical Harry Dym equation.

MSC:

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