The finite-dimensional super integrable system of a super NLS-mKdV equation

Based on the constructed Lie superalgebra, the super Hamiltonian structure of a NLS-mKdV hierarchy is obtained by making use of super-trace identity. Moreover, an explicit super Bargmann symmetry constraint and its associated binary nonlinearization of Lax pairs are carried out for the super NLS-mKdV system.

► The super integrable NLS-mKdV hierarchy is firstly accomplished.
► The super-Bargmann symmetry constraint of the integrable NLS-mKdV hierarchy is constructed.
► The super NLS-mKdV system is decomposed into two finite-dimensional integrable systems.