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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: A new supersymmetric Harry Dym equation is constructed by applying supersymmetric reciprocal transformation to a trivial supersymmetric Harry Dym equation, and its recursion operator and Lax formulation are also obtained. Within the framework of symmetry approach, a class of 3rd order supersymmetric equations of Harry Dym type are considered. In addition to five known integrable equations, a new supersymmetric equation, admitting 5th order generalized symmetry, is shown to be linearizable through supersymmetric reciprocal transformation. Furthermore, its Lax representation and recursion operator are given so that the integrability of this new equation is confirmed. [Copyright &y& Elsevier]

The N = 2 supercomformal transformations are employed to study supersymmetric integrable systems. It is proved that two known N = 2 supersymmetric Harry Dym equations are transformed into two N = 2 supersymmetric modified Korteweg-de Vries equations, thus are connected with two N = 2 supersymmetric Korteweg-de Vries equations. [ABSTRACT FROM AUTHOR]

For the Harry Dym hierarchy, a non-standard Lax formulation is deduced from that of the Korteweg-de Vries (KdV) equation through a reciprocal transformation. By supersymmetrizing this Lax operator, a new N = 2 supersymmetric extension of the Harry Dym hierarchy is constructed, and is further shown to be linked to one of the N = 2 supersymmetric KdV equations through the superconformal transformation. The bosonic limit of this new N = 2 supersymmetric Harry Dym equation is related to a coupled system of KdV-MKdV equations. [ABSTRACT FROM AUTHOR]

Abstract: It is shown that two different supersymmetric extensions of the Harry Dym equation lead to two different negative hierarchies of the supersymmetric integrable equations. While the first one yields the known even supersymmetric Hunter–Saxton equation, the second one is a new odd supersymmetric Hunter–Saxton equation. It is further proved that these two supersymmetric extensions of the Hunter–Saxton equation are reciprocally transformed to two different supersymmetric extensions of the Liouville equation. [Copyright &y& Elsevier]