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

Authors

  • Pinar Albayrak Department of Mathematics, Yildiz Technical University, Istanbul, Turkey
  • Muslum Ozisik Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
  • Mustafa Bayram Department of Computer Engineering, Biruni University, Istanbul, Turkey
  • Aydin Secer Department of Computer Engineering, Biruni University, Istanbul, Turkey
  • Sebahat Ebru Das Department of Mathematics, Yildiz Technical University, Istanbul, Turkey
  • Anjan Biswas Department of Mathematics and Physics, Grambling State University, Grambling, LA, USA
  • Yakup Yıldırım Department of Computer Engineering, Biruni University, Istanbul, Turkey
  • Mohammad Mirzazadeh Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
  • Asim Asiri Mathematical Modeling and Applied Computation Research Group, Center of Modern Mathematical Sciences and their Applications, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

DOI:

https://doi.org/10.37256/cm.4320233308

Keywords:

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

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.

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Published

2023-08-25

How to Cite

1.
Albayrak P, Ozisik M, Bayram M, Secer A, Das SE, Biswas A, Yıldırım Y, Mirzazadeh M, Asiri A. Pure-Cubic Optical Solitons and Stability Analysis with Kerr Law Nonlinearity. Contemp. Math. [Internet]. 2023 Aug. 25 [cited 2024 May 28];4(3):530-48. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3308

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