We study the defocusing nonlinear Schrodinger equation in the quarter plane with asymptotically periodic boundary values. By studying an associated Riemann-Hilbert problem and employing nonlinear steepest descent arguments, we construct solutions in a sector close to the boundary whose leading behaviour is described by a single exponential plane wave. Furthermore, we compute the subleading terms in the long time asymptotics of the constructed solutions.

中文翻译：

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具有渐近时间周期边界值的散焦非线性薛定谔方程解的构造

我们研究了具有渐近周期边界值的四分之一平面中的散焦非线性薛定谔方程。通过研究相关的 Riemann-Hilbert 问题并采用非线性最速下降参数，我们在靠近边界的扇区中构建解决方案，其引导行为由单个指数平面波描述。此外，我们计算了所构造解的长时间渐近线中的子项。