A Super Extension Of Mixed Kn And Akns Hierarchy

In this paper, a super extension of mixed KN and AKNS equation is proposed and its super Bi-Hamiltonian structures and infinitely many conservation laws are constructed, which related to the discrete3×3matrix spectral problem. Starting with the matrix spec-tral problem, a hierarchy of nonlinear differential equations which contains mixed super KN and AKNS as its first unform equation is proposed, with the help of the zero-curvature equation. Then the Hamiltonian structures for the hierarchy are derived from the trace identity. At last, the infinitely many conservation laws of the hierarchy are obtained.