山东大学学报（理学版）
山東大學學報（理學版）
산동대학학보（이학판）
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2008年
8期
82-89
,共8页
规范变换%广义Miura变换%AKNS族
規範變換%廣義Miura變換%AKNS族
규범변환%엄의Miura변환%AKNS족
gauge transformation%general Miura transformation%AKNS hierarchy
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.
立足于一箇2×2譜問題, 推齣瞭一類新的(1+1)維孤子方程族, 對該方程族中的參數取不同的值, 可得到廣義TD族, TD族, 廣義C-KdV和C-KdV, 另外, 此2×2譜問題與AKNS譜問題存在著規範變換, 位勢函數之間也存在廣義Miura 變換, 進而, 兩孤子方程族之間滿足一定的等價關繫.
립족우일개2×2보문제, 추출료일류신적(1+1)유고자방정족, 대해방정족중적삼수취불동적치, 가득도엄의TD족, TD족, 엄의C-KdV화C-KdV, 령외, 차2×2보문제여AKNS보문제존재착규범변환, 위세함수지간야존재엄의Miura 변환, 진이, 량고자방정족지간만족일정적등개관계.
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.
