A super hierarchy of coupled derivative nonlinear Schrِdinger equations and conservation laws

By solving the zero-curvature equation associated with a 3 × 3 matrix spectral problem, a super hierarchy of coupled derivative nonlinear Schrِdinger equations is proposed. The corresponding super bi-Hamiltonian structures are established by means of the super trace identity. Then, we derive infinite conservation laws of the super coupled derivative nonlinear Schrِdinger equation with the aid of spectral parameter expansions.