数学季刊 ›› 2015, Vol. 30 ›› Issue (4): 503-514.doi: 10.13371/j.cnki.chin.q.j.m.2015.04.003
摘要: In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finitedimensional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Finally, we show the decomposition of the soliton equations.
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