DYNAMICS OF OPTICAL WAVE PROFILES TO THE FRACTIONAL THREE-COMPONENT COUPLED NONLINEAR SCHRÖDINGER EQUATION

Usman Younas, Tukur A. Sulaiman, Qasim Ali, Afraz H. Majeed, Krzystof Kedzia and Ahmed Z. Jan
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Usman Younas: Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, P. R. China†Newtouch Center for Mathematics of Shanghai University, Shanghai 200444, P. R. China
Tukur A. Sulaiman: ��Department of Computer Engineering, Biruni University, Istanbul, 34010, Turkey§Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Qasim Ali: �Department of Mathematics, University of Engineering and Technology, Pakistan
Afraz H. Majeed: ��School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, P. R. China
Krzystof Kedzia: *Department of Mechanical Engineering, Wrocław University of Science and Technology, Wrocław, Poland
Ahmed Z. Jan: *Department of Mechanical Engineering, Wrocław University of Science and Technology, Wrocław, Poland

FRACTALS (fractals), 2024, vol. 32, issue 05, 1-13

Abstract: This paper explores the truncated M-fractional three-component coupled nonlinear Schrödinger (tc-CNLS) equation, that regulates the behavior of optical pulses in optical fibers. These equations are utilized in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. The study of multi-component NLS equations has gained significant attention due to their ability to elucidate various complex physical phenomena and exhibit more dynamic structures of localized wave solutions. The freshly invented integration tools, known as the fractional modified Sardar subequation method (MSSEM) and fractional enhanced modified extended tanh-expansion method (eMETEM), are employed to ensure the solutions. The study focuses on extracting various types of optical solitons, including bright, dark, singular, bright-dark, complex, and combined solitons. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. The utilized methodology is effective in explaining fractional nonlinear partial differential equations (FNLPDEs) as it offers pre-existing solutions and additionally derives novel exact solutions by mixing outcomes from various procedures. Furthermore, we plot the visualizations of solutions by plotting 3D, 2D, and contour graphs with the corresponding parameter values. The findings of this paper can improve the understanding of the nonlinear dynamical behavior of a specific system and demonstrate the efficacy of the methodology used. We anticipate that our study will provide substantial benefits to a considerable group of engineering model experts. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

Keywords: Optical Solitons; Fractional Derivative; Modified Sardar Subequation Method; Three-Component Coupled Nonlinear Schrödinger; Enhanced Modified Extended tanh-Expansion (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500865

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