已知部分势函数的AKNS算子的逆谱问题  

Inverse spectral results for AKNS systems with partial information on the potentials

作　　者：孙奕欣 魏广生[1] SUN Yi-xin;WEI Guang-sheng(College of Mathematics and Information Science , Shaanxi Normal University, Xi'an 710119 , Shaanxi , China)

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《山东大学学报（理学版）》2019年第8期50-54,共5页Journal of Shandong University(Natural Science)

摘　　要：考虑定义在[0,1]区间上AKNS算子的逆谱问题。证明了假设2组势函数在区间[a,1](a∈(0,1/2])上已知且它们的差属于Lp空间,若2个系统的共同特征值的数量足够大则这2组势函数相等,且共同特征值的数量与系数p和a有关。We consider the AKNS systems on the interval[0,1] and prove that two potentials already known on [a,1](a∈(0,1/2])and their difference in Lp are equal if the number of their common eigenvalues is sufficiently large. The result here is to write down explicitly this number in terms of p(and a)showing the role of p.

关 键 词：AKNS 系统 势函数 反问题 

分 类 号：O175.1[理学—数学]