Abstract Non-Kerr media possess certain applications in photonic lattices and optical fibers. Studied in this paper are the vector rational and semi-rational rogue waves in a non-Kerr medium, through the coupled cubic-quintic nonlinear Schrodinger system, which describes the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the medium. Applying the gauge transformations, we derive the Nth-order Darboux transformation and Nth-order vector rational and semi-rational rogue wave solutions, where N is a positive integer. With such solutions, we present three types of the second-order rogue waves with the triangle structure: the one with each component containing three four-petaled rogue waves, the one with each component containing three eye-shaped rogue waves, and the other with one component containing three anti-eye-shaped rogue waves and the other component containing three eye-shaped rogue waves. We exhibit the third-order vector rogue waves with the merged, triangle and pentagon structures in each component. Moreover, we show the first- and second-order vector semi-rational rogue waves which display the coexistence of the rogue waves and the breathers.

中文翻译：

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非克尔介质中耦合三次-五次非线性薛定谔系统的矢量有理和半有理流氓波

摘要 非克尔介质在光子晶格和光纤中具有一定的应用。本文通过耦合三次-五次非线性薛定谔系统研究了非克尔介质中的矢量有理和半有理流氓波，描述了五次非线性对介质中超短光脉冲传播的影响。应用规范变换，我们推导出 N 阶 Darboux 变换和 N 阶向量有理和半有理流氓波解，其中 N 是正整数。有了这样的解决方案，我们提出了三种类型的三角形结构的二阶流氓波：一种每个分量包含三个四瓣流氓波，一种每个分量包含三个眼状流氓波，另一个成分包含三个反眼状流氓波，另一个成分包含三个眼状流氓波。我们展示了三阶矢量流氓波，每个组件中都有合并的三角形和五边形结构。此外，我们展示了一阶和二阶向量半理性流氓波，它们显示了流氓波和呼吸者的共存。