Comparative approaches to solving the (2 + 1)-dimensional generalized coupled nonlinear Schrödinger equations with four-wave mixing - Eldidamony, Hanaa A.; Arnous, Ahmed H.; Mirzazadeh, Mohammad; Hashemi, Mir Sajjad; Bayram, Mustafa (Nonlinear Analysis: Modelling and Control, 2025)
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.
Keywords: optical solitons; generalized coupled nonlinear Schrödinger equations; enhanced direct algebraic method; enhanced Kudryashov method; new projective Riccati equation method