与三阶特征值问题相联系的Hamiltonian系统  

The Hamiltonian System Associated with the Third-Order Eigenvalue Problem

作　　者：张俊显[1] 陈兰新[1,2] 王小学[3] 

机构地区：[1]石家庄学院,石家庄050035 [2]中国矿业大学,北京100083 [3]河北工程大学,邯郸056038

出　　处：《大学数学》2010年第4期80-84,共5页College Mathematics

摘　　要：利用特征值问题的非线性化方法,讨论了与三阶特征值问题相联系的Hamiltonian系统,并根据Arnold定理与生成函数方法,证明其在Liouville意义下是完全可积的.然后,借助位势函数与特征函数之间的关系,给出发展方程族的对合解.By means of the nonlinearized Lax pairs,the Hamiltonian system associated with a third-order spectral problem is discussed. Based on the Arnold theorem and the generating function,the Hamiltonian system is completely integrable in the Liouville sense. Moreover,according to the constrained condition between the potential function and the eigenfunction,the involutive solutions of the evolution equations are given.

关 键 词：可积系统 Arnold定理 对合解 

分 类 号：O29[理学—应用数学]