Optical soliton solutions of Gilson pickering equation and modulation instability in optical fiber

Articles in Press

Document Type : Research Paper

Authors

1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.

2 Al-Obour Higher Institute for Engineering and Technology.

10.22034/cmde.2025.66474.3106

Abstract

In this paper, we use the powerful and strong methods to get the solution of Gilson pickering equation known as (H+$\frac{G'(\eta )}{G(\eta )})$ expansion method and ($ \frac{G'(\eta )}{a+b G'(\eta )+G(\eta )}$) expansion method. The performance of these methods is useful and provides us with a lot of new general exact solutions for solving (NPDES). These method is used to solve many problems that occur in physics, fluid physics and optical fiber. Types of solutions are discussed singular, bright and rational. Modulation instability in higher order nonlinear partial differential equations is investigated. Modulation instability is a phenomenon observed in certain types of nonlinear systems, such as in optical fibers or plasma waves. By using linear technique, we establish the modulation instability and show the influence of higher order nonlinear components on modulation instability. Finally, we introduce figures in 2D and 3D. These graphs are very important and useful for describing the behavior of solutions.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 10 April 2026

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History

  • Receive Date: 18 March 2025
  • Revise Date: 14 February 2026
  • Accept Date: 07 April 2026

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