An integrable extension of TD hierarchy and generalized bi-Hamiltonian structures

摘要

A hierarchy of new nonlinear evolution equations associated with 3 x 3 matrix spectral problems are proposed, which is a naturally integrable extension of the TD hierarchy. It is shown that all nonlinear evolution equations in the hierarchy have generalized bi-Hamiltonian structures with the help of the trace identity. Moreover, the infinite sequence of conserved quantities of the first nontrivial equation in the hierarchy is constructed by means of spectral parameter expansion.