与三阶特征值问题相联系的可积系及对合解  

The integrable system related to a third-order eigenvalue problem and involutive solution

作　　者：张俊显[1] 张春花 陈兰新[1] 

机构地区：[1]石家庄学院数学系,河北石家庄050035 [2]衡水广播电视大学理工教研室,河北衡水053000

出　　处：《河北省科学院学报》2007年第4期1-6,共6页Journal of The Hebei Academy of Sciences

摘　　要：基于特征值问题的非线性化方法,得到与三阶特征值问题相联系的有限维系统,利用生成函数证明此系统是L iouville意义下的完全可积系统,并借助可积系统的解,给出发展方程族的解的对合表示。A new type finite-dimensional system associated with a third-order eigenvalue problem is presented by means of the nonlinearized Lax pairs. Based on the generating function of integrals of motion, the resulting system is further improved to be completely integrable in the Liouville sense. Moreover, the involutive solutions of the evolution equations are given.

关 键 词：特征值问题 非线性化 可积系统 对合表示 

分 类 号：O175[理学—数学]