In this paper, we study the inverse scattering problem for energy-dependent Schrodinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions, we transform this scattering problem to the one for non-canonical Dirac systems and show that, in turn, the latter can be placed within the known scattering theory for ZS-AKNS systems. This allows us to give a complete description of the corresponding scattering functions S for the class of problems under consideration and justify an algorithm of reconstructing the problem from S

中文翻译：

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与能量相关的薛定谔方程半线上的逆散射

在本文中，我们研究了半线上与能量相关的薛定谔方程的逆散射问题，在原点处具有与能量相关的边界条件。在某些积极性和非常温和的规律性假设下，我们将这个散射问题转化为非正则 Dirac 系统的问题，并表明后者可以置于 ZS-AKNS 系统的已知散射理论中。这使我们能够为所考虑的问题类别给出相应散射函数 S 的完整描述，并证明从 S 重构问题的算法是合理的