A reliable analytic technique and physical interpretation for the two-dimensional nonlinear Schrödinger equations

Mahmoud A. E. Abdelrahman; H. S. Alayachi; Mahmoud A. E. Abdelrahman; H. S. Alayachi

doi:10.3934/math.20241185

AIMS Mathematics

2024, Volume 9, Issue 9: 24359-24371. doi: 10.3934/math.20241185

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A reliable analytic technique and physical interpretation for the two-dimensional nonlinear Schrödinger equations

Mahmoud A. E. Abdelrahman ^{1,2
,
,},
H. S. Alayachi ¹

1.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

Received: 26 April 2024 Revised: 30 June 2024 Accepted: 08 July 2024 Published: 19 August 2024
MSC : 35C08, 35Q40, 35Q55

Nonlinear Schrödinger equations are a key paradigm in nonlinear research, attracting both mathematical and physical attention. This work was primarily concerned with the usage of a reliable analytic technique in order to solve two models of (2+1)-dimensional nonlinear Schrödinger equations. By applying a comprehensible wave transformation, every nonlinear model was simplified to an ordinary differential equation. A number of critical solutions were observed that correlated to various parameters. The provided approach has various advantages, including reducing difficult computations and succinctly presenting key results. Some 2D and 3D graphical representations regarding presented solitons were considered for the appropriate values of the parameters. We also showed the effect of the physical parameters on the dynamical behavior of the presented solutions. Finally, the proposed approach may be expanded to tackle increasingly complicated problems in applied science.
- two-dimensional nonlinear Schrödinger equations,
- closed-form solutions,
- solitons
Citation: Mahmoud A. E. Abdelrahman, H. S. Alayachi. A reliable analytic technique and physical interpretation for the two-dimensional nonlinear Schrödinger equations[J]. AIMS Mathematics, 2024, 9(9): 24359-24371. doi: 10.3934/math.20241185

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Abstract

Nonlinear Schrödinger equations are a key paradigm in nonlinear research, attracting both mathematical and physical attention. This work was primarily concerned with the usage of a reliable analytic technique in order to solve two models of (2+1)-dimensional nonlinear Schrödinger equations. By applying a comprehensible wave transformation, every nonlinear model was simplified to an ordinary differential equation. A number of critical solutions were observed that correlated to various parameters. The provided approach has various advantages, including reducing difficult computations and succinctly presenting key results. Some 2D and 3D graphical representations regarding presented solitons were considered for the appropriate values of the parameters. We also showed the effect of the physical parameters on the dynamical behavior of the presented solutions. Finally, the proposed approach may be expanded to tackle increasingly complicated problems in applied science.

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