Abstract
In this paper, we study a super Korteweg–de Vries (sKdV) equation proposed by Kupershmidt which possesses a Lax operator with three fully nonlocal terms. The Lax operator is reformulated so that it is of the super constrained modified Kadomtsev–Petviashvili (scmKP) type. By calculating the bi-Hamiltonian structure of the scmKP hierarchy and employing Dirac reduction, we obtain the bi-Hamiltonian structure of the sKdV equation. We also present a spectral problem of its modified system.
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