Hamiltonian structures for nonlinear evolution equations associated with polynomial bundles

For generalized Zakharov–Shabat system, in which the matrixpotential is a polynomial function of the spectral parameter, the generating operator is build up allowing us to rewrite the corresponding nonlinear evolution equations in the compact form. The eigenfunotions of the generating operator are “squares” of the solutions to the initial system. It is shown that the nonlinear evolution equations in question are Hamiltonian one's and the existence of the Hamiltonian structure hierarchy is proved.