A New Finite-dimentional Integrable System Associated To (1+1)-dimentional Solition Equations

In this paper, a new spectral problem is proposed, and nonlinear differential equations of the corresponding hierarchy are obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finite -dimentional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite -dimentional Hamiltonian system is further proved to be completely integrable in the Li-ouville sense. At last, we show the decomposition of the soliton equations.