Analysis of solitary wave solutions in the fractional-order Kundu-Eckhaus system

Saleh Alshammari; Khaled Moaddy; Rasool Shah; Mohammad Alshammari; Zainab Alsheekhhussain; M Mossa Al-Sawalha; Mohammad Yar

doi:10.1038/s41598-024-53330-7

Analysis of solitary wave solutions in the fractional-order Kundu-Eckhaus system

Sci Rep. 2024 Feb 14;14(1):3688. doi: 10.1038/s41598-024-53330-7.

Authors

Saleh Alshammari¹, Khaled Moaddy², Rasool Shah³, Mohammad Alshammari¹, Zainab Alsheekhhussain¹, M Mossa Al-Sawalha¹, Mohammad Yar⁴

Affiliations

¹ Department of Mathematics, College of Science, University of Hail, 2440, Hail, Saudi Arabia.
² Department of Mathematics, College of Science and Humanities, Shaqra University, 11691, Shaqra, Saudi Arabia.
³ Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
⁴ Department of Mathematics, Kabul Polytechnic University, Kabul, Afghanistan. myar@kpu.edu.af.

Abstract

The area of fractional partial differential equations has recently become prominent for its ability to accurately simulate complex physical events. The search for traveling wave solutions for fractional partial differential equations is a difficult task, which has led to the creation of numerous mathematical approaches to tackle this problem. The primary objective of this research work is to provide optical soliton solutions for the Frictional Kundu-Eckhaus equation (FKEe) by utilizing generalized coefficients. This strategy utilizes the Riccati-Bernoulli sub-ODE technique to effectively discover the most favorable traveling wave solutions for fractional partial differential equations. As a result, it facilitates the extraction of optical solitons and intricate wave solutions. The Backlund transformation is used to methodically construct a sequence of solutions for the specified equations. The study additionally showcases 3D and Density graphics that visually depict chosen solutions for certain parameter selections, hence improving the understanding of the outcomes.