Nonlinear Superintegrable Couplings for Supercoupled KDV Hierarchy with Self-Consistent Sources

In this paper, based on matrix Lie superalgebras, a new isospectral super-Lax matrix is established. By employing the super-Ablowitz–Kaup–Neweu–Segur (AKNS) scheme nonlinear superintegrable couplings for the supercoupled KdV hierarchy are worked out. Supertrace identity is used to furnish super-Hamiltonian structures for the superintegrable hierarchy. Furthermore, we propose nonlinear superintegrable couplings of the resulting integrable hierarchy with self-consistent sources.