Li-Zhuang 族的推广及相关的 Neum ann 和 Bargm ann 系统(英文)

Neumann and Bargmann Systems Associated with an Extension of Li Zhuang Hierarchy

提出 Ｌｉ Ｚｈｕａｎｇ 族的一种推广，适当选取特征值问题中的参考函数可得到许多新的非线性发展方程族．利用迹的恒等式建立起这些新族的双 Ｈａｍ ｉｌｔｏｎ 结构． 在 Ｎｅｕｍ ａｎｎ 和 Ｂａｒｇｍ ａｎｎ 约束下，将特征值问题非线性化为有限维 Ｈａｍ ｉｌｔｏｎ

An extension of Li Zhuang hierarchy is discussed.We present new problems of a kind,for which many new hierarchies of nonlinear evoluation equations are derived by choosing different reference functions in the eigenvalue problem.The bi Hamiltonian structure of the corresponding hierarchies is obtained by using the trace identity.Under the so called Neumann and Bargmann constraints between the potentials and the eigenfunctions,the eigenvalue problem is nonlinearized as to finite dimensional Hamiltonian systems.