Coupled Nonlinear Schrödinger Equations for Pulse Interactions in Optical Fibers: Self- and Cross-Phase Modulation Effects

Ngla Farag Mhmoud-Meriki , Abdulmalik.A.Altwaty

Department of Mathematics, Faculty of Science, University of Benghazi, AL Marj, Libya

Email: ngla.meriki@uob.edu.ly

HNSJ, 2024, 5(11); https://doi.org/10.53796/hnsj511/14

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Published at 01/11/2024 Accepted at 20/10/2024

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Abstract

In this paper, we explore the pulse interactions in optical fibers governed by the Coupled Nonlinear Schrödinger Equations (CNLSEs), considering both self- and cross-phase modulation effects. These equations play a crucial role in understanding the dynamics of pulse propagation in nonlinear optical media, especially in scenarios involving multiple interacting pulses. To investigate this, we apply the -Expansion Method, a powerful analytical technique for deriving exact solutions to nonlinear differential equations. By employing this method, we derive a family of explicit traveling wave solutions, expressed in terms of hyperbolic, trigonometric, and rational functions. These solutions provide valuable insight into the physical phenomena associated with the interaction of pulses in optical fibers, such as the modulation and stability of pulse envelopes. The results demonstrate the effectiveness of the -Expansion Method in solving complex coupled systems and contribute to a deeper understanding of nonlinear optical effects, with potential applications in optical communication systems and pulse shaping technologies. Numerical simulations are presented to illustrate the behavior of the obtained solutions under different parameter settings, highlighting the significance of self- and cross-phase modulation in pulse dynamics.

Key Words: Coupled Nonlinear Schrödinger Equations (CNLSEs); Pulse interactions; Self- and cross-phase modulation; The -expansion method; Optical fibers.

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