Optical Solitons for the Fokas-Lenells Equation with Beta and M-Truncated Derivatives

Abstract

The Fokas-Lenells equation (FLE) including the M-truncated derivative or beta derivative is examined. Using the modified mapping method, new elliptic, hyperbolic, rational, and trigonometric solutions are created. Also, we extend some previous results. Since the FLE has various applications in telecommunication modes, quantum field theory, quantum mechanics, and complex system theory, the solutions produced may be used to interpret a broad variety of important physical process. We present some of 3D and 2D diagrams to illustrate how M-truncated derivative and the beta derivative influence the exact solutions of the FLE. We demonstrate that when the derivative order decreases, the beta derivative pushes the surface to the left, whereas the M-truncated derivative pushes the surface to the right.