Study of fractional nonlinear Schr¨odinger equation for soliton solutions

Abstract

The fact that nonlinear partial differential equations (NLPDEs) are used in practically ev- ery academic domain including biology, chemistry, physics, mechanics, fiber optics, at- mospheric science, and electronics research makes them significant. One special kind of NLPDE is the nonlinear Schr¨odinger equation (NLSE), research in the fields of engineer- ing, biology, and physics has uses for the NLSE. A major subject of nonlinear model re- search during the past 20 years has been the soliton, an essential description in the NLSE analysis. Particularly, the development of optical solitons has given nonlinear optics a the- oretical foundation. In the framework of the time-fractional cubic-quintic nonlinear Schr¨odinger equation (TFCQ- NLSE), the analysis of soliton solutions is the main emphasis of this work. Wide-ranging applications of this adaptive model can be found in many complicated real phenomena, such as fiber optic communication, nonlinear optics, optical signal processing, laser-tissue interaction in medical science, and many others. The intensity of the cubic and quintic non- linear components determines the observed nonlinear effects, which include self-focusing, self-phase modulation, and wave-mixing. This model’s investigation employs a robust analytical approach. Our sub-ode approach, will be multitude of potential solitons and furnishes details on the interactions of laser pulses, was employed to explore this model. This inquiry yields numerous illustrated soliton solutions. Among these solutions are those that are hyperbolic, rational, singular, bright, Jacobian elliptic solutions (JES), Weierstrass elliptic solutions (WES) and periodic solutions (PS)