Two types of smooth positons for nonlocal Fokas-Lenells equation

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. 2 and 3. 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.