带有幂函数的AKNS族及其Neumann流  

AKNS hierarchy with power function and its Neumann flow

作　　者：蒋志民[1] 

机构地区：[1]商丘师范学院数学系,河南商丘476000

出　　处：《商丘师范学院学报》2000年第6期43-47,共5页Journal of Shangqiu Normal University

基　　金：河南省自然科学基金!(9940 51700);河南省教委科研资助项目!(1999110017)

摘　　要：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 。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.

关 键 词：AKNS族 干扰函数 发展方程 NEUMANN系统 非线性 

分 类 号：O175.29[理学—数学]