数学物理学报 ›› 2012, Vol. 32 ›› Issue (2): 424-432.

• 论文 • 上一篇    下一篇

超AKNS方程新的可积分解

季杰1|虞静2|董亚娟1   

  1. 1.浙江工商大学统计与数学学院 杭州 |310018|
    2.杭州电子科技大学数学系 杭州 310018
  • 收稿日期:2010-11-28 修回日期:2011-10-15 出版日期:2012-04-25 发布日期:2012-04-25
  • 基金资助:

    国家自然科学基金(10926036, 11026087, 11001069, 61003207)、浙江省教育厅科技项目(Y200906909, Y201017468)和浙江省自然科学基金(Y6090172, Y6100126, Y6100588)资助

Novel Integrable Decomposition of the Super AKNS Equation

 JI Jie1, YU Jing2, DONG Ya-Juan1   

  1. 1.College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018;
    2.Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2010-11-28 Revised:2011-10-15 Online:2012-04-25 Published:2012-04-25
  • Supported by:

    国家自然科学基金(10926036, 11026087, 11001069, 61003207)、浙江省教育厅科技项目(Y200906909, Y201017468)和浙江省自然科学基金(Y6090172, Y6100126, Y6100588)资助

摘要:

该文介绍从3×3矩阵形式超谱问题出发, 构造新高阶矩阵形式超谱问题的方法. 以超AKNS方程为例, 作者构造了5×5矩阵形式的超AKNS谱问题并且运用双非线性化方法, 给出了超AKNS方程的新约束, 得到该约束下超AKNS方程新的可积分解.

关键词: 超谱问题, 可积分解,  , 超AKNS方程

Abstract:

In this paper, the approach to construct higher super matrix spectral problems from a 3×3 super matrix spectral problem is presented. As an example, we construct a 5×5 super spectral problem which is associated with the super AKNS equation from the 3×3 super AKNS spectral problem, by  use of the binary nonlinearization method, new constraint of super AKNS equation is obtained. The corresponding  new integrable decomposition of the super AKNS equation is presented also.

Key words: Super spectral problem,  Integrable decomposition, Super AKNS equation

中图分类号: 

  • 37K10