New lump solutions to the nonlinear Schrödinger equation under the few-cycle pulse propagation property

Throughout this work, we will derive new various types of lump solutions to the nonlinear Schrödinger equation that describing few-cycle pulse propagation in metamaterials. The propagation of waves through optical fibre is one of recent phenomenon that plays fundamental rule in all telecommunication processes as well as medicine devices industries, ocean engineering devices technologies. The lump solutions of this model will be firstly constructed in this article via three various techniques which are the (G’/G)-expansion method, the extended simple equation method (ESEM) and the Paul-Painleve approach method (PPAM). These three techniques have been regularly implemented in parallel paths to show the agreements between the output results. When the comparison between our achieved results with each other’s as well as by that achieved previously has been implemented, it shows the novelty of these results.