The integrability and parametric representation of a hierarchy of soliton equations

The parametric representation for finite-band solutions of a stationary soliton equation is discussed. This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense. The nonconfocal involutive integral representations {F m } are obtained also. The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.