带有幂函数的AKNS族及其Neumann流

考虑带有幂函数干扰的ＡＫＮＳ等谱问题，仍然成功地导出一族新的非线性发展方程族，并利用迹的恒等式建立起这一非线性发展方程族的双Ｈａｍｉｌｔｏｎ结构，在势和特征函数之间的Ｎｅｕｍａｎｎ约束之下，我们将等谱问题非线性化为有限维Ｈａｍｉｌｔｏｎ系统。

AKNS hierarchy with power function and its Neumann flow

By giving an isospectral problem properly.One can relate it to a hierarchy of nonlinear evolution equations.Inserting a reference function into AKNS hierarchy,We have obtained several new hierarchies of nonlinear evolution equations.In this paper.A new eigenvalue problem with power function as an interferential function is discussed,from which a new hierarchy of nonlinear evolution equations is derived sucessfully.The bi Hamiltonian form of the corresponding hierarchy is obtained by using the trace identity.It is shown also that under so called Neumann constraint between the potentials and the eigenfunctions,the ergenvalue problem is nonlinearized as finite dimensional Hamiltonian systems many results had before become special cases of this paper.