Lie-Poisson结构下一个新的有限维完全可积系统

A New Finite-dimensional Integrable System in the Lie-Poisson Framework

研究3×3谱问题的非线性化,证明了该系统的非线性化特征值问题是具有Lie-Poisson结构的Poisson流形R3N上的广义Hamilton系统.进一步,利用母函数法给出其可积性的证明.

The nonlinearization of a 3×3 spectral problem is presented.It is shown that this nonlinearized eigenvalue problem is a generalized Hamiltonian system with Lie-Poisson structure on the Poisson manifold R3N.Further,its integrability is given by the generating function method.