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

Pinar Albayrak, Muslum Ozisik, Mustafa Bayram, Aydin Secer, Sebahat Ebru Das, Anjan Biswas, Yakup Yıldırım*, Mohammad Mirzazadeh, Asim Asiri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)530-548
Number of pages19
JournalContemporary Mathematics (Singapore)
Volume4
Issue number3
DOIs
Publication statusPublished - 2023
Externally publishedYes

Keywords

  • Vakhitov-Kolokolov slope condition
  • auxiliary equation method
  • impact of the dispersion
  • optical soliton
  • pure-cubic soliton

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