New solitary solutions to the nonlinear Schrodinger equation under the few-cycle pulse propagation property

Throughout this work, three different methodologies namely the the (G'/G)-expansion method, the extended simple equation method and the Paul-Painleve approach method were introduced, to offer a variety of novel analytical solutions to the nonlinear Schrodinger equation that describes few-cycle pulse propagation in metamaterials. The obtained results predict many types of solutions including the bright-like soliton solutions, dark-like soliton solutions, double-bright soliton as M-shaped and W-shaped, perfect periodic soliton solutions, singular periodic soliton solutions and other rational solitons solutions. The suggested model is important one that describes the propagation of waves through optical fibre which is one of recent phenomena that plays fundamental rule in all telecommunication processes as well as medicine devices industries, ocean engineering devices technologies. The distinct solutions that were constructed in this article have been demonstrated for the first time via the above three various techniques. These three techniques have been regularly implemented in parallel paths to show the agreements between the output results. When we implement the comparison between our Owen achieved results each with other as well as by that achieved previously by Abbagari et al. (Eur Phys J Plus 136:710, 2021) who solved special case of this model and (Rezazadeh in Optik 167:218-227, 2018; Salathiel et al. in Optik 197:163108, 2019; Yao et al. in AIP Adv 11:065218, 2021; Inc in Optik 138, 1-7, 2017)) who applied different techniques the novelty of our achieved results will be detected.