Lie-Poisson框架下一个新的Hamilton系统的可积性

Integrability of a New Hamiltonian System in the Lie-Poisson Framework

研究一个3×3形式的谱问题的非线性化,证明了该3×3特征值问题的非线性化是具有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 eigenvalue problem is presented. It is shown that this nonlinearized eigenvalue problem is a generalized Hamiltonian system with a Lie-Poisson structure on the Poisson manifold R3N.Further,its integrability is proved by the generating function method.