Abstract
In this article, the closed form general and standard solutions accessible in the literature of nonlinear evolution equation (NLEE), namely, the Fokas-Lenells (FL) equation is established by using the generalized Kudryashov approach. The implemented method extracts lots of new and compatible wave solutions involving unknown parameters and expressed in terms of exponential, trigonometric and hyperbolic functions. We explain the physical meaning of geometrical structures for some derived solutions by assigning definite values of the unspecified parameters. As an aftermath, diverse wave shapes including kink wave shape, flat kink wave shape, bell shape, anti-bell shape, singular bell shape along with bright, dark, singular solitary wave envelopes are properly developed. These nonlinear wave envelopes are frequently applicable in optical fibers. It has been established that the assigned techniques are general, efficient and straightforward and also it can be exerted to accomplish closed form solutions of diverse NLEEs originated in mathematical physics and engineering fields.