与广义KdV方程族相关的谱问题及其完全可积性  

The Spectral Problem Related to the Generalized KdV Equations and Its Completely Integrable System

作　　者：孙海珍[1] 刘亚峰[1] 

机构地区：[1]石家庄铁道大学数理系

出　　处：《石家庄铁道大学学报（自然科学版）》2013年第1期106-110,共5页Journal of Shijiazhuang Tiedao University(Natural Science Edition)

摘　　要：通过Lax方程获得了与二阶谱问题相联系的广义KdV方程族。利用位势函数与特征函数之间的Bargmann约束,将Lax对非线性化。由合适的Jacobi-Ostrogradsky坐标,得到一个新的有限维Hamilton正则系统,并证明其是完全可积系统。最后得到发展方程族的对合表示。Based on the Lax equation, the generalized KdV equations hierarchy related to the 2th-order eigenvalue problem is given. By the Bargmann constraint between the potentials and the eigenvector functions, the Lax pairs are ninlinearized. Using a reasonable Jacobi-Ostrogradsky coordinate, a new finite-dimensional Hamilton canonical equations are obtained, and proved to be completely integrable systems. Moreover, the involutive solutions of the evolution equations are given.

关 键 词：谱问题 非线性化 Bargmann约束 可积系统 

分 类 号：O175.9[理学—数学]