我们处理声波逆散射问题，用于探测远源场图（Far Field Map）中混合边界条件干扰。结果显示几何特性和材料参数的表面分布与干扰的数值重建有关。本项研究主要是在我们近期完成的探针指示函数和复值表面阻抗的高阶渐进展开式的理论工...我们处理声波逆散射问题，用于探测远源场图（Far Field Map）中混合边界条件干扰。结果显示几何特性和材料参数的表面分布与干扰的数值重建有关。本项研究主要是在我们近期完成的探针指示函数和复值表面阻抗的高阶渐进展开式的理论工作的基础上进一步进行数值分析和实现。基于极小范数解，展开更多
The prolongation structure technique of Wahlquist and Estanbrook is improved and applied to a newequation proposed by Z.J.Qiao [J.Math.Phys.48 (2007) 082701].Two potentials and two pseudopotentials areobtained,from wh...The prolongation structure technique of Wahlquist and Estanbrook is improved and applied to a newequation proposed by Z.J.Qiao [J.Math.Phys.48 (2007) 082701].Two potentials and two pseudopotentials areobtained,from which a new type of inverse scattering problem,Lax equations,and infinite number of conservation lawsare obtained.展开更多
简介
Ludwig Faddeev（路德维希·法捷叶夫）教授对于数学和理论物理学的贡献使他广为人知．他的这些贡献重塑了现代的数理物理学（Mathematical Physics）．他在量子场论（QFT）方面的工作给在1970年代发生的规范场理论的革命奠...简介
Ludwig Faddeev（路德维希·法捷叶夫）教授对于数学和理论物理学的贡献使他广为人知．他的这些贡献重塑了现代的数理物理学（Mathematical Physics）．他在量子场论（QFT）方面的工作给在1970年代发生的规范场理论的革命奠定了基础，而他对量子力学中多体问题以及对逆散射问题的贡献属于这个领域中的最深刻成就．展开更多
The paper is concerned with the reconstruction of a defect in the core of a two-dimensional open waveguide from the scattering data. Since only a finite numbers of modes can propagate without attenuation inside the co...The paper is concerned with the reconstruction of a defect in the core of a two-dimensional open waveguide from the scattering data. Since only a finite numbers of modes can propagate without attenuation inside the core, the problem is similar to the one-dimensional inverse medium problem. In particular, the inverse problem suffers from a lack of uniqueness and is known to be severely ill-posed. To overcome these difficulties, we consider multi-frequency scattering data. The uniqueness of solution to the inverse problem is established from the far field scattering information over an interval of low frequencies.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 11075055, 61021004, 10735030the Shanghai Leading Academic Discipline Project, China under Grant No. B412the Program for Changjiang Scholars and the Innovative Research Team in University of Ministry of Education of China under Grant No. IRT 0734
文摘The prolongation structure technique of Wahlquist and Estanbrook is improved and applied to a newequation proposed by Z.J.Qiao [J.Math.Phys.48 (2007) 082701].Two potentials and two pseudopotentials areobtained,from which a new type of inverse scattering problem,Lax equations,and infinite number of conservation lawsare obtained.
文摘简介
Ludwig Faddeev（路德维希·法捷叶夫）教授对于数学和理论物理学的贡献使他广为人知．他的这些贡献重塑了现代的数理物理学（Mathematical Physics）．他在量子场论（QFT）方面的工作给在1970年代发生的规范场理论的革命奠定了基础，而他对量子力学中多体问题以及对逆散射问题的贡献属于这个领域中的最深刻成就．
基金supported by National Science Foundation of USA(Grant Nos.DMS0908325DMS-0968360 and DMS-1211292)+2 种基金Ofce of Naval Research of USA(ONR)(Grant No.N00014-12-10319)National Natural Science Foundation of China(Grant No.91130004)the grant UJF-MSTIC-Plasmons
文摘The paper is concerned with the reconstruction of a defect in the core of a two-dimensional open waveguide from the scattering data. Since only a finite numbers of modes can propagate without attenuation inside the core, the problem is similar to the one-dimensional inverse medium problem. In particular, the inverse problem suffers from a lack of uniqueness and is known to be severely ill-posed. To overcome these difficulties, we consider multi-frequency scattering data. The uniqueness of solution to the inverse problem is established from the far field scattering information over an interval of low frequencies.
