Pure-Cubic Optical Solitons and Stability Analysis with Kerr Law Nonlinearity

In this research paper, we investigate the effects of third-order dispersion and nonlinear dispersion terms on soliton behavior for pure-cubic solitons in the absence of chromatic dispersion. The research proceeds in several stages. First, we derive the nonlinear ordinary differential equation form by utilizing the complex wave transform. In the second stage, we employ a simplified version of the new extended auxiliary equation method to derive both bright and singular optical solitons. Subsequently, we examine the influence of model parameters on these bright and singular solitons in the third stage. To support our findings, we present solution functions accompanied by effective graphical simulations. We report observations regarding the effects of parameters in the relevant sections. The validity of our results is confirmed through their satisfaction of the model equation. Furthermore, we apply the Vakhitov-Kolokolov stability criterion to ensure the stability of the obtained bright soliton solution. Notably, the novelty of this paper lies in its application of a simplified version of the extended auxiliary equation approach to recover optical solitons. This study stands apart from previously published works that utilized various expansion approaches, yielding a distinct spectrum of results.

Automated summary

In this research, the effects of third-order dispersion and nonlinear dispersion on pure-cubic solitons in the absence of chromatic dispersion are investigated. The research involves deriving the nonlinear ordinary differential equation form, deriving both bright and singular optical solitons using a simplified version of the extended auxiliary equation method, examining the influence of model parameters on these solitons, and validating the results. The novelty of this paper lies in its application of a simplified version of the extended auxiliary equation approach to recover optical solitons.