Abstract
This manuscript uses the generalized Khater (GK) method and the trigonometric quintic B-spline (TQBS) scheme to study the calculations and approximate solutions of complex nonlinear Fokas-Lenells (FL) equations. This model describes the propagation of short pulses in optical fibers. Many novel computing solutions have been obtained. The absolute, real, and imaginary values of some solutions are plotted in two three-dimensional and density graphs to explain the dynamic behavior of short pulses in the fiber. The use of constructed analytical solutions to evaluate initial and boundary conditions allows the application of numerical solutions to study the accuracy of our novel computational techniques. The performance of both methods demonstrates the ability, effectiveness, and ability to apply them to different forms of nonlinear evolution equations to check the accuracy of analytical and numerical solutions.