Alshammari Saleh, Moaddy Khaled, Shah Rasool, Alshammari Mohammad, Alsheekhhussain Zainab, Al-Sawalha M Mossa, Yar Mohammad
Department of Mathematics, College of Science, University of Hail, 2440, Hail, Saudi Arabia.
Department of Mathematics, College of Science and Humanities, Shaqra University, 11691, Shaqra, Saudi Arabia.
Sci Rep. 2024 Feb 14;14(1):3688. doi: 10.1038/s41598-024-53330-7.
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.
分数阶偏微分方程领域最近因其能够精确模拟复杂物理事件的能力而备受瞩目。寻找分数阶偏微分方程的行波解是一项艰巨的任务，这促使人们创造了众多数学方法来解决这个问题。本研究工作的主要目标是通过利用广义系数为摩擦Kundu-Eckhaus方程（FKEe）提供光学孤子解。该策略利用Riccati-Bernoulli子常微分方程技术有效地发现分数阶偏微分方程最有利的行波解。因此，它有助于提取光学孤子和复杂波解。Backlund变换用于系统地构造特定方程的一系列解。该研究还展示了三维和密度图形，直观地描绘了某些参数选择下的选定解，从而增进了对结果的理解。
