LAUSR

The Darboux transformation for the coupled Fokas–Lenells equations and the special vector solution of the corresponding Lax pair are constructed. Utilizing a limiting process, some novel high-order semirational solutions of the coupled system are given. They include high-order rogue waves interacting with multi-bright or dark solitons, and high-order rogue waves interacting with multi-breathers. Also, the dynamic structures of the first- and second-order semirational solutions are discussed. Furthermore, it is shown that the free parameter $$\gamma $$γ in the special vector solution can influence the interactional processes (fusion or separation) among different nonlinear waves. Compared to the uncoupled systems, there may exist more abundant and interesting solutions in the coupled ones.