Hybrid accurate simulations for constructing some novel analytical and numerical solutions of three-order GNLS equation

Abstract

This study presents analytical and numerical solutions of a simplified third-order generalized nonlinear Schrödinger equation (GNLSE) to demonstrate how ultrashort pulses behave in optical fiber and quantum fields. The investigated model can be used as a wave model to illustrate the wave aspect of the matter. It is called a quantum-mechanical state function because it might show how atoms and transistors move and act physically. Four analytical and numerical schemes are used to construct an accurate novel solution. Khater II (Kha II) and novel Kudryashov (NKud) methods are present in the employed analytical scheme. In contrast, the exponential cubic-B-spline and trigonometric-quantic-B-spline schemes represent the simulated numerical techniques. Many novel solitary wave solutions are constructed and formulated in some distinct forms and represented through density, three-, and two-dimensional graphs. The built analytical solutions accuracy is investigated by deriving the requested boundary and initial conditions for implementing the suggested numerical schemes that show the matching between both solutions (analytical and numerical). This matching between solutions proves the accuracy of the obtained solutions. Additionally, to guarantee the applicability of our solutions, we investigate their stability by using the Hamiltonian systems properties. Finally, the novelty of our study and its scientific contributions are illuminated by comparing our results with recently published ones.