Inverse scattering theory for Schrödinger operators with steplike potentials

Inverse scattering theory for Schrödinger operators with steplike potentials
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阶梯势薛定谔算子的逆散射理论

DOI：
10.15407/mag11.02.123
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发表时间：
2015
期刊：
arXiv: Spectral Theory
影响因子：
--
通讯作者：
G. Teschl
G. Teschl
中科院分区：
--
文献类型：
--
作者：
I. Egorova;Z. Gladka;Till Luc Lange;G. Teschl

文献摘要

被引文献

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研究了具有阶梯势的一维薛定谔方程的正、逆散射问题，给出了散射数据对应于给定光滑度和给定衰减到其渐近性的势的充要条件，这些结果对于利用逆散射变换求解KDV方程具有重要意义.
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed smoothness and prescribed decay to their asymptotics. These results are important for solving the Korteweg-de Vries equation via the inverse scattering transform.