一族孤立子系统的规范变换(英文)  

Gauge transformation for a kind of soliton hierarchy

作　　者：王燕[1] 张义宁[2] 杜殿楼[3] 

机构地区：[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

出　　处：《山东大学学报（理学版）》2008年第8期82-89,共8页Journal of Shandong University(Natural Science)

基　　金：Supported by the National Natural Science Foundation of China(19801016,10261003).

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。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 wansformafion 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 Mium transformation between the potential functions of the two hierarchies was also given.

关 键 词：规范变换 广义Miura变换 AKNS族 

分 类 号：O29[理学—应用数学]