On Analytical And Numerical Simulations For The Ultra-Short Pulses Mathematical Model In Optical Fibers

This paper investigates the solitons and breathers wave solutions of the generalized nonlinear Schrödinger equation (NLGSE) of third order through new generalized computational (generalized Khater (GK)) technique. These solutions are employed to construct the initial and boundary conditions to apply a new numerical scheme known by the trigonometric Quintic spline. This well-known mathematical model in ultra-short pulses in the engineering and applied sciences, especially optical fibers, where the obtained solutions can be used in distinct applications. The NLGSE is the basis of the mechanical wave model, which helps in studying the structure of the atom, and as the name suggests, it shows all the wave-like properties of matter. Also, it is considered a state function of a quantum-mechanical system that describes the atoms’ dynamical and physical behavior, or transistors where it determines the atomic particle at a specific position and time. In fact, this approach is sometimes regarded as a platform for quantum aspects. The accuracy of our solutions is checked by evaluating the absolute error value between functional and numerical solutions. In addition, the physical representations of the model under consideration are represented in some of the solutions obtained graphically. The consequences of empirical and computational methods are confirmed by the accuracy and uniqueness of their tests.