一个n×n矩阵特征值问题的迹公式及其应用  

The Trace Formula of an n×n Matrix Eigenvalue Problem and Its Application

作　　者：张广耀[1] 李镇[1] 

机构地区：[1]郑州大学数学系,河南郑州450001

出　　处：《郑州大学学报（理学版）》2010年第4期18-23,共6页Journal of Zhengzhou University:Natural Science Edition

摘　　要：研究一个n×n矩阵特征值问题,得到了与之相应的孤子方程族及迹公式.通过对该特征值问题及其伴随问题和迹公式求泛函导数,得到了位势与特征函数间的约束关系,进而得到了位势的特征函数表示,这正是Bargmann约束,从而该特征值问题被非线性化为Liouville完全可积的Hamilton系统.An n×n matrix eigenvalue problem is studied, and the associated soliton hierarchy and the trace formulae are obtained. By taking functional derivatives of the eigenvalue problem and its adjoint one and the trace formula, the constraint between the potentials and eigenfunctions is de- rived. Thus the eigenfunctions expressions of the potentials are obtained, which is just the Bargmann constraint. Hence, the eigenvalue problem is nonlinearized to a completely integrable Hamiltonian system in Liouville sense.

关 键 词：特征值问题 迹公式 非线性化 完全可积系统 

分 类 号：O175.3[理学—数学]