A Hierarchy of New Nonlinear Evolution Equations and Their Bi-Hamiltonian Structures

A hierarchy of new nonlinear evolution equations associated with a 3×3 matrix spectral problem with four potentials is proposed, in which two typical members are a new coupled Burgers equation and a new coupled KdV equation. The bi-Hamiltonian structures for the hierarchy of nonlinear evolution equations are established by using the trace identity.