In this paper, the coupled Fokas–Lenells equations which describe the propagation of ultrashort optical pulses in birefringent fibers are transformed into a nonlinear ordinary differential equation system by using a suitable similarity transformation. Then, the nonlinear ordinary differential equation is solved by the trial equation technique. As a result, many new kink, bell, periodic and rational solitary wave structures are yielded. Some figures are given to illustrate the differences between pulses propagation in 3D and 2D dimensional. [ABSTRACT FROM AUTHOR]