数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 251-258.

• 论文 • 上一篇    下一篇

Kaup-Newell方程族等谱和一阶非等谱之间的规范变换

薛玉山   

  1. 中央财经大学 统计与数学学院 北京 100081
  • 收稿日期:2012-08-20 修回日期:2013-12-24 出版日期:2014-04-25 发布日期:2014-04-25

Gauge Transformation Between the Isospectral and First-Order Nonisospectral Kaup-Newell Hierarchies

 XUE Yu-Shan   

  1. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081
  • Received:2012-08-20 Revised:2013-12-24 Online:2014-04-25 Published:2014-04-25

摘要:

通过引入等谱和一阶非等谱Ablowitz-Kaup-Newell-Segur系统, 得到了等谱Kaup-Newell(KN)谱问题和一阶非等谱KN谱问题的规范变换, 并建立了等谱和一阶非等谱KN方程族之间的等价关系.

关键词: Kaup-Newell系统, 规范变换, 等谱Kaup-Newell方程族, 非等谱Kaup-Newell方程族

Abstract:

In this paper, the gauge transformation between the isospectral and first-order nonisospectral Kaup-Newell (KN) spectral problems is derived by introducing the isospectral and first-order nonisospectral Ablowitz-Kaup-Newell-Segur system. Besides, the equivalence relation between the isospectral and first-order nonisospectral KN hierarchies is given.

Key words: Kaup-Newell system, Gauge transformation, Isospectral KN hierarchies, Nonisospectral hierarchies

中图分类号: 

  • 34A34