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| 一族孤立子系统的规范变换 | |
| 引用本文： | 王燕,张义宁,杜殿楼.一族孤立子系统的规范变换[J].山东大学学报(理学版),2008,43(8):82-89. |
| 作者姓名： | 王燕 张义宁 杜殿楼 |
| 作者单位： | 1. 洛阳师范学院数学科学学院,河南,洛阳,471000 2. 聊城大学数学系,山东,聊城,252000 3. 郑州大学数学系,河南,郑州,450052 |
| 摘 要： | 立足于一个2×2谱问题, 推出了一类新的(1+1)维孤子方程族, 对该方程族中的参数取不同的值, 可得到广义TD族, TD族, 广义C-KdV和C-KdV, 另外, 此2×2谱问题与AKNS谱问题存在着规范变换, 位势函数之间也存在广义Miura 变换, 进而, 两孤子方程族之间满足一定的等价关系。 |
| 关 键 词： | 规范变换 广义Miura变换 AKNS族 |
Gauge transformation for a kind of soliton hierarchy |
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| WANG Yan,ZHANG Yi-ning,DU Dian-lou.Gauge transformation for a kind of soliton hierarchy[J].Journal of Shandong University,2008,43(8):82-89. | |
| Authors: | WANG Yan ZHANG Yi-ning DU Dian-lou |
| Institution: | 1. College of Mathematics Science, Luoyang Normal University, Luoyang 471022, Henan, China;2. Department of Mathematics, Liaocheng University, Liaocheng 252000, Shangdong, China;3. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, Henan, China |
| Abstract: | Based on a 2×2 eigenvalue problem, a new 1+1 dimensional soliton hierarchy was presented. By choosing some special values of parameters in the hierarchy, the hierarchies of the TD, generalized TD, the C-KdV and generalized C-KdV were obtained. Furthermore, a gauge transformation for this 2×2 eigenvalue problem was given, and through this transformation, the 2×2 hierarchy was gauged equivalent to the AKNS hierarchy, and also, the generalized Miura transformation between the potential functions of the two hierarchies was also given. |
| Keywords: | gauge transformation general Miura transformation AKNS hierarchy |
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