Novel dispersive soliton solutions to a fractional nonlinear Schrödinger equation related with ultrashort pulses

Abstract

In this study, the third-order fractional nonlinear Schrödinger equation (3-FNLS), which is crucial in fibre optics, is discussed. The equation models propagation of light in optical fibres when ultrashort pulses are generated. In order to explain the physical phenomena, beta, conformable and M-truncated fractional derivative operators are considered. Exact solutions were sought using the extended modified auxiliary equation mapping method (EMAEM). Three-dimensional (3D) and two-dimensional (2D) graphics were designed for each fractional derivative operator of several solutions corresponding to various fractional order values. These graphics were used to study the behaviour of the solutions for conformable, beta and M-truncated fractional derivative operators and to make significant comparisons.