A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures

With the aid of the zero-curvature equation, a hierarchy of new nonlinear evolution equations is proposed, which is associated with a 3 × 3 matrix spectral problem with four potentials. The generalized bi-Hamiltonian structures for the hierarchy are derived by using the trace identity. Furthermore, we construct the infinite conservation laws of a typical nonlinear evolution equation in the hierarchy by utilizing spectral parameter expansion.