We consider the Cauchy problem for the integrable nonlocal nonlinear Schrödinger equation , with a step-like boundary values: as and as for all , where is a constant. In a recent paper, we presented the long-time asymptotics of the solution of this problem along the rays , where is a constant. In the present paper, we extend the asymptotics into a region that is asymptotically closer to the ray than any of these rays. We specify a one-parameter family of wedges in the -plane, with curved boundaries, characterized by qualitatively different asymptotic behavior of , and present the main asymptotic terms for each wedge. Particularly, for wedges within , we show that the solution decays as with depending on the wedge. For wedges within , we show that the asymptotics has an oscillatory nature, with the phase functions specific for each wedge and depending on a slow variable parameterizing the wedges.

中文翻译：

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可积非局部非线性薛定谔方程的长期渐近曲线中的曲线楔形

我们考虑可积非局部非线性薛定谔方程的柯西问题，其具有阶跃边界值：as和as for all ，其中是常数。在最近的一篇论文中，我们提出了该问题沿射线的解的长时间渐近性，其中是常数。在本文中，我们将渐近线扩展到比任何这些射线都更接近射线的区域。我们在平面中指定了一个单参数的楔形族，具有弯曲的边界，特征在于 的渐近行为在性质上不同，并呈现每个楔形的主要渐近项。特别是，对于内的楔子，我们表明，该解决方案衰变与取决于楔形。对于 内的楔形，我们表明渐近性具有振荡性质，具有特定于每个楔形的相位函数并取决于对楔形进行参数化的慢变量。