Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber

Jamshad Ahmad; Sonia Akram; Kanza Noor; Muhammad Nadeem; Amelia Bucur; Yahya Alsayaad

doi:10.1038/s41598-023-37757-y

Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber

Sci Rep. 2023 Jul 5;13(1):10877. doi: 10.1038/s41598-023-37757-y.

Authors

Jamshad Ahmad¹, Sonia Akram¹, Kanza Noor¹, Muhammad Nadeem², Amelia Bucur³, Yahya Alsayaad⁴

Affiliations

¹ Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, 50700, Pakistan.
² School of Mathematics and Statistics, Qujing Normal University, Qujing, 655011, China. nadeem@mail.qjnu.edu.cn.
³ Department of Mathematics and Informatics, Faculty of Sciences, "Lucian Blaga" University of Sibiu, 550012, Sibiu, Romania.
⁴ Department of Physics and Mathematics, Zabid-Hodeidah, Hodeidah University, Al-Hudaydah, 4113, Yemen. yahyaalsayyad2022@hoduniv.net.ye.

Abstract

In this research, we study traveling wave solutions to the fractional extended nonlinear SchrÖdinger equation (NLSE), and the effects of the third-order dispersion parameter. This equation is used to simulate the propagation of femtosecond, plasma physic and in nonlinear optical fiber. To accomplish this goal, we use the extended simple equation approach and the improved F-expansion method to secure a variety of distinct solutions in the form of dark, singular, periodic, rational, and exponential waves. Also, the stability of the outcomes is effectively examined. Several graphs have been sketched under appropriate parametric values to reinforce some reported findings. Computational work along with a graphical demonstration confirms the exactness of the proposed methods. The issue has not previously been investigated by taking into account the impact of the third order dispersion parameter. The main objective of this study is to obtain the different kinds of traveling wave solutions of fractional extended NLSE which are absent in the literature which justify the novelty of this study. We believe that these novel solutions hold a prominent place in the fields of nonlinear sciences and optical engineering because these solutions will enables a through understanding of the development and dynamic nature of such models. The obtained results indicate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable traveling wave solutions to nonlinear equations emerging in various branches of scientific, technological, and engineering domains.