Abstract
Two different schemes are applied to the generalized nonlinear Fokas-Lennells equation for obtaining possible optical solitonic solutions at general orders of nonlinearities. It is known that the standard Kudryashov method leads to singular combo optical soliton solutions, but only for some particular orders of nonlinearities. The new extended Kudryashov method, developed in this study, is able to derive soliton solutions at general orders of nonlinearity. Furthermore, a singular optical soliton solution is achieved by the Riccati equation method in addition to three forms of plane wave solutions under some constraints on the physical parameters. The obtained solutions via this later method are more general than those mentioned in the present-day literature.