Abstract
In this paper, by utilizing logarithmic transformation and symbolic computation with the ansatz function technique, we investigated the rational solitons of the Fokas-Lenells equation. We obtained two types of M-shaped rational solitons and their dynamics are shown in figures by selecting the appropriate values of involved parameters. Furthermore, two types of interactions of M-shaped rational solitons with kink waves are investigated. We obtained the novel structures and very interesting interactional phenomena of M-shaped rational solitons with kink waves.