A new version of trial equation method for a complex nonlinear system arising in optical fibers

• Published in: Optical and quantum electronics Vol. 56; no. 6
• Main Authors: Kirci, Ozlem, Pandir, Yusuf, Latifa, Agamalieva, Bulut, Hasan
• Format: Journal Article
• Language: English
• Published: New York Springer US 03-05-2024
• Subjects: Characterization and Evaluation of Materials; Computer Communication Networks; Electrical Engineering; Lasers; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Analytical methods; Fokas system; Exact traveling wave solution; New version of trial equation method
• ISSN: 1572-817X; 1572-817X
• DOI: 10.1007/s11082-024-06825-6

In this study, the dissipation problem of nonlinear pulse in mono mode optical fibers which is governed by the Fokas system (FS) is considered. The solutions of this system have an important role in comprehending the different wave structures in physical settings. Therefore, a new version of the trial equation method (NVTEM) is employed to present the new exact wave solutions of the FS. The advantage of the NVTEM is to use different root possibilities of a polynomial which shape the solutions of the related model. Primarily this system is converted to a nonlinear ordinary differential equation (NODE) via the traveling wave transform to apply the proposed method. Various exact wave solutions to the FS are obtained such as rational function, exponential function, hyperbolic function, and Jacobi elliptic function solutions. Thus, we have revealed solutions featly which are unlike the wave solutions previously found by other analytical methods. The present results depict the formation and development of such waves and their interactions. The exhibition of the solutions is given by 3D plots together with the corresponding 2D plots. The outcomes have shown that the proposed technique is abundant in achieving different wave solutions of many nonlinear differential equations in the field of optics.