Abstract
We propose a generalized super Camassa-Holm equation, which is completely integrable in the sense of admitting of a Lax pair and a bi-Hamiltonian structure. Through Dirac reduction, we obtain a bi-Hamiltonian structure of the super Camassa-Holm equation introduced by Geng, Xue and Wu [Stud. Appl. Math. 130 (2013) 1-16]. By introducing an appropriate reciprocal transformation, we connect the generalized super Camassa-Holm equation with a negative generalized super KdV equation, which is also equipped with a Lax pair and a bi-Hamiltonian structure.
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