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

• A super hierarchy of the coupled derivative non-linear Schrödinger is constructed.
• The super bi-Hamiltonian structure associated with the super hierarchy is established.
• The infinite many conservation laws are investigated.

By solving the zero-curvature equation associated with a 3 × 3 matrix spectral problem, a super hierarchy of coupled derivative nonlinear Schrödinger 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 Schrödinger equation with the aid of spectral parameter expansions.