一个能量与位势相依的二阶谱问题及其相关的发展方程族  

The Second-order Spectral Problem of Energy Depended on Potential and Hierarchy of Evolution Equations

作　　者：张瑞君[1] 刘亚峰[2] 

机构地区：[1]河北工业大学理学院,天津300401 [2]石家庄铁道大学数理系,河北石家庄050043

出　　处：《石家庄铁道大学学报（自然科学版）》2016年第4期105-108,共4页Journal of Shijiazhuang Tiedao University(Natural Science Edition)

摘　　要：本文将研究一个二阶谱系及相关的非线性发展方程及其Hamilton系统,利用Lax对非线性化方法,讨论经典力学的Jacobi-Ostrogradsky坐标,得到Bargmann约束下完全可积的Hamilton系统,通过Bargmann约束,从而给出发展方程族解的对合表示。In this paper, the nonlinear evolution equation and the Hamilton system related to a sec- ond-order spectral problem are studied. Using the nonlinearization approach of Lax pairs, the Jacobi-Os- trogradsky coordinates of classical mechanics is discussed. Finally the completely integrable Hamilton system can be obtained in the Bargmann constraint condition, and the involutive solutions of the evolu- tion equations are given.

关 键 词：谱问题 Lax对非线性化 Bargmann约束 可积系统 

分 类 号：O175.9[理学—数学]