Novel solitary wave solutions of the (3+1)–dimensional nonlinear Schrödinger equation with generalized Kudryashov self–phase modulation

Nafissa Toureche Trouba; Mohamed E. M. Alngar; Reham M. A. Shohib; Haitham A. Mahmoud; Yakup Yildirim; Huiying Xu; Xinzhong Zhu; Nafissa Toureche Trouba; Mohamed E. M. Alngar; Reham M. A. Shohib; Haitham A. Mahmoud; Yakup Yildirim; Huiying Xu; Xinzhong Zhu

doi:10.3934/math.2025202

AIMS Mathematics

2025, Volume 10, Issue 2: 4374-4411. doi: 10.3934/math.2025202

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Novel solitary wave solutions of the (3+1)–dimensional nonlinear Schrödinger equation with generalized Kudryashov self–phase modulation

1.
School of Computer Science and Technology, Zhejiang Normal University, Jinhua, 321004, China
2.
Zhejiang Institute of Photoelectronics, Jinhua, Zhejiang 321004, China
3.
Department of Mathematics Education, Faculty of Education & Arts, Sohar University, Sohar 3111, Oman
4.
Basic Science Department, Higher Institute of Management Sciences & Foreign Trade, Cairo, 379, Egypt
5.
Industrial Engineering Department, College of Engineering, King Saud University, Riyadh 11421, Saudi Arabia
6.
Department of Computer Engineering, Biruni University, Istanbul–34010, Turkey
7.
Mathematics Research Center, Near East University, 99138 Nicosia, Cyprus
8.
College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou 325035, China

Received: 24 December 2024 Revised: 09 February 2025 Accepted: 18 February 2025 Published: 28 February 2025
MSC : 35Q55, 35Q60, 35Q61

This paper investigates the (3+1)-dimensional nonlinear Schrö dinger equation, incorporating cross-spatial dispersion and a generalized form of Kudryashov's self-phase modulation. Using the generalized Jacobi elliptic method, we systematically derive novel soliton solutions expressed in terms of Jacobi elliptic and Weierstrass elliptic functions, providing deeper insights into wave dynamics in nonlinear optical media. The obtained solutions exhibit diverse structural transformations governed by the parameter (n) known as full nonlinearity, encompassing optical bullet solutions, optical domain wall solutions, singular solitons, and periodic solutions. Furthermore, we discuss the potential experimental realization of these solitonic structures in ultrafast fiber lasers and nonlinear optical systems, drawing connections to recent experimental findings. To facilitate a comprehensive understanding of their physical properties, we present detailed three-dimensional (3D), two-dimensional (2D), and contour visualizations, highlighting the interplay among dispersion, nonlinearity, and self-modulation effects. These results offer new perspectives on soliton interactions and have significant implications for optical communication, signal processing, and nonlinear wave phenomena.
- novel solitons,
- cross-spatio-dispersion,
- generalized Jacobi elliptic method
Citation: Nafissa Toureche Trouba, Mohamed E. M. Alngar, Reham M. A. Shohib, Haitham A. Mahmoud, Yakup Yildirim, Huiying Xu, Xinzhong Zhu. Novel solitary wave solutions of the (3+1)–dimensional nonlinear Schrödinger equation with generalized Kudryashov self–phase modulation[J]. AIMS Mathematics, 2025, 10(2): 4374-4411. doi: 10.3934/math.2025202

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Abstract

This paper investigates the (3+1)-dimensional nonlinear Schrö dinger equation, incorporating cross-spatial dispersion and a generalized form of Kudryashov's self-phase modulation. Using the generalized Jacobi elliptic method, we systematically derive novel soliton solutions expressed in terms of Jacobi elliptic and Weierstrass elliptic functions, providing deeper insights into wave dynamics in nonlinear optical media. The obtained solutions exhibit diverse structural transformations governed by the parameter (n) known as full nonlinearity, encompassing optical bullet solutions, optical domain wall solutions, singular solitons, and periodic solutions. Furthermore, we discuss the potential experimental realization of these solitonic structures in ultrafast fiber lasers and nonlinear optical systems, drawing connections to recent experimental findings. To facilitate a comprehensive understanding of their physical properties, we present detailed three-dimensional (3D), two-dimensional (2D), and contour visualizations, highlighting the interplay among dispersion, nonlinearity, and self-modulation effects. These results offer new perspectives on soliton interactions and have significant implications for optical communication, signal processing, and nonlinear wave phenomena.

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