Abstract
Abstract The super integrable system and its super Hamiltonian structure are established based on a loop super Lie algebra and super-trace identity in this paper. Then the super integrable system with self-consistent sources and conservation laws of the super integrable system are constructed. Furthermore, an explicit Bargmann symmetry constraint and the binary nonlinearization of Lax pairs for the super integrable system are established. Under the symmetry constraint,the n $n$ -th flow of the super integrable system is decomposed into two super finite-dimensional integrable Hamilton systems over the supersymmetric manifold. The integrals of motion required for Liouville integrability are explicitly given.
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