论文标题
依赖能量的schrödinger方程的半线上的反向散射
Inverse scattering on the half-line for energy-dependent Schrödinger equations
论文作者
论文摘要
在本文中，我们研究了一半的能量依赖性schrödinger方程的逆散射问题，其原点处具有能量依赖性边界条件。在某些积极性和非常轻度的规律性假设下，我们将此散射问题转换为非规范狄拉克系统的散射问题，并表明，后者又可以将后者放置在ZS-AKNS系统的已知散射理论中。这使我们可以完整描述所考虑的问题类别的相应散射功能s，并证明从S中重建问题的算法是合理的
In this paper, we study the inverse scattering problem for energy-dependent Schrödinger 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
