Abstract
For a class of super skew-symmetric operators with eight parameters, two kinds of super Hamiltonian operators are identified by the method of functional multi-vectors. Appropriate decompositions of these operators lead to compatible super Hamiltonian pairs which in turn produce nonlinear super bi-Hamiltonian systems from the trivial x-translation flow. As examples, besides the super Korteweg–de Vries equations and other known ones, new super generalizations are obtained for the Riemann equation, the Hunter–Saxton equation and the Camassa–Holm equation, all of them admit two compatible local super Hamiltonian operators.
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