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Abstract In this paper, the Fokas–Lenells (FL) equations are investigated via bilinear approach. We bilinearize the unreduced FL system, derive double Wronskian solutions, and then, by means of a reduction technique we obtain variety of solutions of the reduced equations. This enables us to have a full profile of solutions of the classical and nonlocal FL equations. Some obtained solutions are illustrated based on asymptotic analysis. As a notable new result, we obtain solutions to the FL equation, which are related to real discrete eigenvalues and not reported before in the analytic approaches. These solutions behave like (multi)periodic waves or solitary waves with algebraic decay. In addition, we also obtain solutions to the two‐dimensional massive Thirring model from those of the FL equation.
Liu et al. (Mon,) studied this question.