The admissibility of the initial-boundary data, which characterizes the existence of solution for the initial-boundary value problem, is important. Based on the Fokas method and the inverse scattering transformation, an approach is developed to solve the initial-boundary value problem of the nonlinear Schrödinger equation on a finite interval. A necessary and sufficient condition for the admissibility of the initial-boundary data is given, and the reconstruction of the potential is obtained.

中文翻译：

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非线性薛定谔方程在有限区间上可解的一个充要条件

初始边界数据的可接受性很重要，它表征了初始边界值问题的解的存在性。基于Fokas方法和逆散射变换，提出了一种求解有限区间非线性薛定谔方程初边值问题的方法。给出了初始边界数据可接受性的充要条件，得到了势能的重构。