Optical solitons of improved perturbed nonlinear Schrödinger equation with cubic-quintic-septic and triple-power laws in optical metamaterials

Abstract

Abstract Purpose. This paper aims to extract optical solitons of improved perturbed nonlinear Schrödinger equations (IP-NLSE) with cubic-quintic-septic (CQS) and a triple-power law (TP-law) using the new Kudryashov and the extended sinh-Gordon equation expansion (eShGEE) methods. Methodology. First, we apply a wave transformation to the studied equations to generate the nonlinear ordinary differential equation (NLODE) form. Next, by computing the balancing constant in the NLODE form, we use the new Kudryashov and eShGEE methods to obtain the equation’s solution in the NLODE form. We get an algebraic equation system on the NLODE by replacing the suggested solution function and its derivatives in the NLODE form. With the help of the solutions of the system, we are able to determine the appropriate solution sets for unknown parameters. Substituting these sets and wave transforms into the proposed solution functions by the new Kudryashov and eShGEE methods, we get the solutions for the problems under investigation. Findings. We have successfully obtained soliton solutions for the considered equations and plotted 3D and 2D graphs of the derived solution functions. In addition to obtaining the soliton solutions, we present some graphical investigation of the impact of the parameters in the considered equations. Originality. To our best knowledge, the improved perturbed nonlinear Schrödinger equations with CQS and a triple-power law have not been studied before. It is also innovative to examine how the equation’s parameters affect the soliton’s behavior. In this regard, the study’s findings are novel, and it is anticipated that they will advance research in the area.