  In this paper, the Fokas-Lenells equations are investigated via bilinear
approach. We bilinearize the unreduced Fokas-Lenells 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 Fokas-Lenells equations.
Some obtained solutions are illustrated based on asymptotic analysis. As a
notable new result, we obtain solutions to the Fokas-Lenells 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 Fokas-Lenells
equation.
