Abstract
A super hierarchy of the vector nonlinear Schrödinger equations associated with the 3 × 3 matrix spectral problem is proposed by using the Lenard recursion equations and the zero-curvature equation. The corresponding super bi-Hamiltonian structures are established with the help of the super trace identity. Furthermore, we derive the infinite conservation flows of the super vector nonlinear Schrödinger equation and the second equation in the hierarchy by utilizing spectral parameter expansions.
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