In this paper, we investigate breather positons and higher-order rogue waves for the nonlocal Fokas-Lenells equation. In this nonlocal optical system, rogue waves can be generated when periods of breather positons go to infinity. In addition, we find two very interesting phenomena: one is that rogue waves sitting on a periodic line wave background are derived; the other is that a hybrid of rogue waves and a periodic kink wave is also constructed. We believe that these interesting findings exist in the optical system corresponding to the nonlocal Fokas-Lenells equation.

中文翻译：

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非局部Fokas-Lenells方程的呼吸正气和流浪

在本文中，我们研究了非局部Fokas-Lenells方程的呼吸正电子和高阶流浪。在这种非局部光学系统中，当呼吸正电子的周期达到无限远时，可能会产生恶意波。此外，我们发现了两个非常有趣的现象：一是派生出位于周期线波背景上的无赖波；二是在波峰背景上产生了无赖波。另一个是还构造了流氓波和周期性扭结波的混合体。我们相信这些有趣的发现存在于与非局部Fokas-Lenells方程相对应的光学系统中。