In this paper, we propose a new type of smooth positon called novel rational positon. Similar to classic smooth positons, the modulus square of novel rational positons can also be decomposed. But there is a fundamental difference between classic smooth positons and novel rational positons in terms of algebraic structure and dynamical properties. Specific propositions and conclusions are given in Secs. [Formula: see text] and [Formula: see text]. Further, these two types of smooth positons sitting on a periodic line wave background are derived for the first time. In addition, a new nonlinear superposition between these two types of smooth positions and a kink soliton is constructed.

中文翻译：

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非局部 Fokas-Lenells 方程的两种光滑位置

在本文中，我们提出了一种新型的光滑位置，称为新有理位置。与经典光滑位置类似，新有理位置的模平方也可以分解。但就代数结构和动力学性质而言，经典光滑位置和新颖有理位置之间存在根本区别。具体的命题和结论在 Secs 中给出。[公式：见正文]和[公式：见正文]。进一步地，首次推导出了这两种位于周期线波背景上的光滑位置。此外，在这两种类型的光滑位置和扭结孤子之间构造了一个新的非线性叠加。