Computational and approximate solutions of complex nonlinear Fokas-Lenells equation arising in optical fiber

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.

Automated summary

This manuscript explores the calculations and approximate solutions of complex nonlinear Fokas-Lenells equations using the generalized Khater method and the trigonometric quintic B-spline scheme. The obtained novel computing solutions are plotted in graphs to explain the dynamic behavior of short pulses in optical fibers. The constructed analytical solutions are used to evaluate initial and boundary conditions and apply numerical solutions to study the accuracy of the novel computational techniques, demonstrating the effectiveness and versatility of the methods in analyzing nonlinear evolution equations.