The constraints of potentials and the finite-dimensional integrable systems

Abstract

Restricting potential to the space spanned by the eigenvectors of the recursion operator leads to a natural constraint of potential and a finite-dimensional integrable Hamiltonian system. The general method for proving the consistency of the two systems stemming from the Lax pair and obtaining the constants of the motion for the Hamiltonian system is illustrated by the classical Boussinesq and AKNS hierarchies. By using gauge transformation, similar results for the Jaulent–Miodek and Kaup–Newell hierarchies are presented.