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Abstract: 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. [Copyright &y& Elsevier]

Abstract: In this Letter, we present a bi-Hamiltonian structure for the two-component Novikov equation. We also show that proper reduction of this bi-Hamiltonian structure leads to the Hamiltonian operators found by Hone and Wang for the Novikov equation. [Copyright &y& Elsevier]

Studies the Hamiltonian theory for two-component AKNS hierarchy and Yajima-Oikawa hierarchy from the viewpoint of reduction. Hamiltonian structures of the AKNS showing a Dirac equation of the sl(3) current algebra; Relationship of the Yajima-Oikawa hierarchy to the classical W[sub 4][sup (3)] algebra.

In this paper, a super extension of Sawada–Kotera hierarchy is proposed. This hierarchy is derived by considering a third order Lax operator with a weakly nonlocal term. Bi-Hamiltonian structure is constructed for the super Sawada–Kotera hierarchy. [ABSTRACT FROM AUTHOR]