Optical solitons for Radhakrishnan–Kundu–Lakshmanan equation in the presence of perturbation term and having Kerr law

Abstract

Purpose: In this research study, obtaining the analytical and soliton solutions to the perturbed Radhakrishnan–Kundu–Lakshmanan (RKL) equation with Kerr law nonlinearity is aimed via the generalized projective Riccati equations method (GPREM), a simple version of the new extended auxiliary equation method (SAEM26), and unified Riccati equation expansion method (UREEM). At the same time, the roles of some parameters included in the perturbed RKL equation on soliton dynamics are analyzed. Methodology: The presented methods are successfully employed to the perturbed RKL equation. In the application of the presented methods, to convert the perturbed RKL equation into a nonlinear ordinary differential equation, we choose suitable complex wave transformation for the proposed model. Later, a linear equation system is derived using the GPREM, SAEM26, and UREEM, the system is solved, the appropriate solution sets are obtained, and the soliton solutions are achieved, respectively. Findings: The singular, bright and dark soliton solutions are generated by choosing the suitable set and parameter values. To comprehend the physical dynamics of some solutions, 3D, contour, and 2D graphs are demonstrated. In addition, 2D graphs are drawn to show how some parameters in the main equation have an effect on soliton behaviors. The examination indicates that the model parameters have a substantial effect on the soliton dynamics. Depending on the soliton forms, the effect can be varied. The results presented in this paper will be useful for future works in soliton theory and the presented methods can be effectively implemented to such equations. Originality: The effects of the model parameters included in the perturbed RKL equation on soliton dynamics are analyzed for the first time in this study.