On new abundant solutions of the complex nonlinear Fokas–Lenells equation in optical fiber

Variational method is important since it can reduce the order of the differential equation to make the equation simpler and obtain the optimal solution by the stationary condition. In this paper, we mainly study the complex nonlinear Fokas–Lenells equation (CNFLE), which is used to describe the propagation of short pulses in optical fibers. The traveling wave transformation is used to convert the CNFLE into the ODE, and the variational principle of the solution is obtained by the semi‐inverse method. Based on the variational principle, the extended He′s variational method, which is based on the Ritz‐like method, is employed to investigate the bright soliton, bright‐like soliton, bright–dark soliton, and periodic wave solution. The absolute, real, and imaginary parts of the novel computational solutions are plotted through one example in the form of 3‐D and 2‐D contours. In addition, the physical explanation of the solutions is elaborated in detail. The results reveal that the variational method is straightforward, simple, and effective, which is expected to bring a light to the study of the traveling wave theory.