New polynomial involutive system and a classical complexity integrable system (Q1210268)

The authors consider the eigenvalue problem \[ y_ x = \left({- \lambda+v\atop u-v}\quad{u+v\atop \lambda-v}\right)y,\quad y={y_ 1\choose y_ 2}.\tag{1} \] They give the Lax pairs for evolution equation hierarchy in relation to (1), and then nonlinearize the Lax systems by introducing certain constraint conditions between the potentials and the eigenfunctions and constructing a new polynomial involutive system, in order to prove that the nonlinearized form of (1) is a complete integrable Hamiltonian system in the Liouville sense.