Abstract
In this paper, we will focus on the reverse space–time Fokas–Lenells equation. According to the Lax pair, the semi-degenerate Darboux transformation will be constructed by Taylor expansions. Based on the determinant form, some rogue wave solutions will be derived on the three types of backgrounds, including M-shaped periodic waves, mixed M-shaped periodic waves and breather, mixed single-periodic and double-periodic waves. And the rogue waves in various backgrounds can be transformed into the corresponding backgrounds waves with parameters selection. The dynamic features of those solutions will be discussed via graphical illustration. It is worth mentioning that these results are novel.
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