Comparative approaches to solving the (2 + 1)-dimensional generalized coupled nonlinear Schrödinger equations with four-wave mixing
Articles
Hanaa A. Eldidamony
Higher Technological Institute
Ahmed H. Arnous
El Shorouk Academy
https://orcid.org/0000-0002-7699-7068
Mohammad Mirzazadeh
University of Guilan
Mir Sajjad Hashemi
University of Bonab
Mustafa Bayram
Biruni University
https://orcid.org/0000-0002-2994-7201
Published 2025-01-02
https://doi.org/10.15388/namc.2025.30.38324
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Keywords

optical solitons
generalized coupled nonlinear Schrödinger equations
enhanced direct algebraic method
enhanced Kudryashov method
new projective Riccati equation method

How to Cite

Eldidamony, H.A. (2025) “Comparative approaches to solving the (2 + 1)-dimensional generalized coupled nonlinear Schrödinger equations with four-wave mixing”, Nonlinear Analysis: Modelling and Control, 30(1), pp. 83–107. doi:10.15388/namc.2025.30.38324.

Abstract

This paper extensively studies the propagation of optical solitons within the framework of (2 + 1)-dimensional generalized coupled nonlinear Schrödinger equations. The investigation employs three worldly integration techniques: the enhanced direct algebraic method, the enhanced Kudryashov method, and the new projective Riccati equation method. Through the application of these methods, a broad spectrum of soliton solutions has been uncovered, including bright, dark, singular, and straddled solitons. Additionally, this study reveals solutions characterized by Jacobi andWeierstrass elliptic functions, enriching the understanding of the dynamics underpinning optical solitons in complex systems. The diversity of the soliton solutions obtained demonstrates the versatility and efficacy of the employed integration techniques and contributes significantly to the theoretical and practical knowledge of nonlinear optical systems.

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