Novel optical soliton solutions for the generalized integrable (2+1)- dimensional nonlinear Schrödinger system with conformable derivative

Muhammad Bilal; Javed Iqbal; Ikram Ullah; Aditi Sharma; Hasim Khan; Sunil Kumar Sharma; Muhammad Bilal; Javed Iqbal; Ikram Ullah; Aditi Sharma; Hasim Khan; Sunil Kumar Sharma

doi:10.3934/math.2025497

AIMS Mathematics

2025, Volume 10, Issue 5: 10943-10975. doi: 10.3934/math.2025497

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Research article

Novel optical soliton solutions for the generalized integrable (2+1)- dimensional nonlinear Schrödinger system with conformable derivative

1.
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, Pakistan
2.
School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
3.
Department of Computer Science and Engineering, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune, India
4.
Department of Mathematics, College of Science, Jazan University, P. O. Box 114, Jazan 45142, Saudi Arabia
5.
Department of Information Systems College of Computer and Information Sciences Majmaah University, Majmaah 11952, Saudi Arabia

Received: 01 March 2025 Revised: 21 April 2025 Accepted: 27 April 2025 Published: 13 May 2025
MSC : 65F10, 65H10, 90C30, 90C33

For the generalized integrable (2+1)-dimensional nonlinear Schrödinger system, new and creative analytical solutions were derived using a novel extended direct algebraic method incorporating conformable derivatives, which could be expressed in terms of elementary functions and yielded a variety of analytical solutions, such as single, optical periodic, and wave solitons. The analytical solutions provided key insights into the effects of conformable derivatives and temporal parameters on the behavior of optical solitons, such as their stability, propagation, and interaction. To further elucidate the dynamics of these solitons, 2D, 3D, and contour plots were created to provide a visual representation of the soliton's form, amplitude, and phase. This helps to better understand the behavior of the soliton and its potential applications in nonlinear equations. Based on the study's demonstration of the extended direct algebraic method's strength and versatility in obtaining analytical solutions for complex non linear systems, it may be a useful tool for solving a variety of nonlinear problems in science and engineering.
- extended Direct algebraic approach,
- conformable derivatives,
- nonlinear system,
- analytical solutions,
- generalized integrable nonlinear Schrödinger system
Citation: Muhammad Bilal, Javed Iqbal, Ikram Ullah, Aditi Sharma, Hasim Khan, Sunil Kumar Sharma. Novel optical soliton solutions for the generalized integrable (2+1)- dimensional nonlinear Schrödinger system with conformable derivative[J]. AIMS Mathematics, 2025, 10(5): 10943-10975. doi: 10.3934/math.2025497

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Abstract

For the generalized integrable (2+1)-dimensional nonlinear Schrödinger system, new and creative analytical solutions were derived using a novel extended direct algebraic method incorporating conformable derivatives, which could be expressed in terms of elementary functions and yielded a variety of analytical solutions, such as single, optical periodic, and wave solitons. The analytical solutions provided key insights into the effects of conformable derivatives and temporal parameters on the behavior of optical solitons, such as their stability, propagation, and interaction. To further elucidate the dynamics of these solitons, 2D, 3D, and contour plots were created to provide a visual representation of the soliton's form, amplitude, and phase. This helps to better understand the behavior of the soliton and its potential applications in nonlinear equations. Based on the study's demonstration of the extended direct algebraic method's strength and versatility in obtaining analytical solutions for complex non linear systems, it may be a useful tool for solving a variety of nonlinear problems in science and engineering.

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