具有Miura势的薛定谔算子的线上逆散射，II。不同的Riccati代表
Inverse scattering on the line for Schrödinger operators with Miura potentials, II. Different Riccati representatives
摘要：
这是第二次在一系列文件散射理论的一维薛定谔运营商与三浦潜力承认Riccati表示形式$q=u'+u^2$的一些$u\in L^2(R)$。我们认为潜在的存在“左”和“右”Riccati代表规定的半线上的可积性。这个类包括所有的Faddeev-Marchenko势在$L^1(R,(1+|x|)dx)$产生积极的薛定谔算子，以及许多与狄拉克δ函数和库仑类奇点的分布势。我们完整地描述了相应的一组反射系数$r$和证明的算法重建$q$从$r$。
英文摘要：
This is the second in a series of papers on scattering theory for one-dimensional Schrödinger operators with Miura potentials admitting a Riccati representation of the form $q=u'+u^2$ for some $u\in L^2(R)$. We consider potentials for which there exist `left' and `right' Riccati representatives with prescribed integrability on half-lines. This class includes all Faddeev--Marchenko potentials in $L^1(R,(1+|x|)dx)$ generating positive Schrödinger operators as well as many distributional potentials with Dirac delta-functions and Coulomb-like singularities. We completely describe the corresponding set of reflection coefficients $r$ and justify the algorithm reconstructing $q$ from $r$.
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