Reconstruction of Singularities of a Scattering Potential in Two Dimensions

Reconstruction of Singularities of a Scattering Potential in Two Dimensions
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二维散射势奇点的重构

DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
E. Somersalo
E. Somersalo
中科院分区：
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文献类型：
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作者：
L. Päivärinta;V. Serov;E. Somersalo

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本文考虑二维薛定谔方程的逆散射问题。从远场数据重建散射势的问题有一个众所周知的近似解，它是基于弱散射体（或玻恩）近似的线性化。本文的研究表明，虽然该近似解不需要接近底层散射势，但该方法可以准确地恢复势的局部奇异性。
In this paper, we consider the inverse scattering problem for the Schrodinger equation in two dimensions. This problem of reconstructing the scattering potential from the far field data has a well-known approximate solution based on the linearization through the weak scatterer (or Born) approximation. In the present work it is shown that while this approximate solution need not be close to the underlying scattering potential, the leading local singularities of the potential are recovered exactly in this procedure.