带二阶位势四阶Schrödinger算子的反散射问题  

Inverse Scattering Problem for the Fourth Order Schrödinger Operator with the Second Order Potential

作　　者：黄华 李会珍 HUANG Hua;LI Huizhen(School of Information Engineering,Wuhan College,Wuhan 430212,China;School of Mathematical and Physical Sciences,Wuhan Textile University,Wuhan 430200,China;Research Center for Applied Mathematics and Interdisciplinary Sciences,Wuhan Textile University,Wuhan 430200,China)

机构地区：[1]武汉学院信息工程学院,湖北武汉430212 [2]武汉纺织大学数理科学学院,湖北武汉430200 [3]武汉纺织大学应用数学与交叉科学研究中心,湖北武汉430200

出　　处：《应用数学》2024年第4期971-981,共11页Mathematica Applicata

基　　金：湖北省教育厅科学技术研究计划指导性项目(B2021365);湖北省自然科学基金指导性项目(2022CFC065);湖北省高校优秀中青年科技创新团队(T2022055);2023年度武汉学院科研基金(JJB202304)。

摘　　要：本文研究带二阶位势的四阶Schrödinger算子的反散射问题,利用复几何光学解构造的方法,证明四阶Schrödinger算子的散射矩阵可以唯一确定二阶位势、一阶位势和零阶位势,将四阶Schrödinger算子反散射问题的结果从带一阶位势推广到了带二阶位势.This paper concerns the inverse scattering problem for the fourth order Schrödinger operator with a second order potential.Using the method of construction of the complex geometric optical,we show that the scattering matrix of the fourth order Schrödingeroperator can uniquely determines the second order potential,the first order potential and the zero order potential,which extends the early results from the first order potential to the second order potential of the fourth order Schrödinger operator in this problem.

关 键 词：四阶Schrödinger算子 反散射问题 二阶位势 复几何光学解 

分 类 号：O175.29[理学—数学]