Computational investigation on a nonlinear dispersion model with the weak non-local nonlinearity in quantum mechanics

Ying-zi, Jiang; Wang, Fuzhang; Salama, Samir A.; Botmart, Thongchai; Khater, Mostafa M. A.

doi:10.1016/j.rinp.2022.105583

Cited by 32 publications

(4 citation statements)

References 28 publications

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“…Nonlinear partial differential equations (NLPDEs) [1][2][3] appear in a variety of fields of science and engineering, including fluid dynamics [4], heat transfer [5], electromagnetism [6], quantum mechanics [7], and more. They often arise in situations where the underlying physical phenomena exhibit nonlinear behavior, such as turbulence [8], shock waves [9], and pattern formation [10].…”

Section: Introductionmentioning

confidence: 99%

Optical soliton solutions of the perturbed fourth-order nonlinear Schrödinger-Hirota equation with parabolic law nonlinearity of self-phase modulation

Altun,

Secer,

Ozisik

et al. 2024

Phys. Scr.

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This article introduces an examination of optical soliton solutions for the perturbed fourthordernonlinear Schr¨odinger-Hirota equation, which plays a crucial role in optics. For the firsttime, it utilizes a novel approach by applying the extended auxiliary equation method. Thisequation models the propagation of optical pulses through nonlinear media, such as opticalfibers, and has been the subject of many studies. Our goal extends beyond merely acquiringa significant number of soliton solutions using the method described in this article; we alsoaim to investigate the impact of the coefficients of group velocity dispersion, parabolic law,and fourth-order dispersion terms on soliton propagation in the problem examined. The 2D,3D, and contour plots of the acquired dark and bright solitons, which represent the mostfundamental soliton types, are presented. Additionally, all other calculations are performedusing symbolic algebraic software. The results provide us with valuable insights, confirmingthat the introduced model can be analyzed from a physical perspective. It is demonstratedthat the proposed technique is not only important but also efficient in analyzing variousnonlinear scientific problems.

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Section: Introductionmentioning

confidence: 99%

Optical soliton solutions of the perturbed fourth-order nonlinear Schrödinger-Hirota equation with parabolic law nonlinearity of self-phase modulation

Altun,

Secer,

Ozisik

et al. 2024

Phys. Scr.

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show abstract

“…As a result, fractional-order NLPDEs have garnered attention in recent studies, particularly in optics and other applied sciences, owing to their potential applications in modeling highly nonlinear phenomena [22][23][24]. Fractional-order derivatives offer advantages over integer derivatives, providing more accurate mathematical and physical models for various technical issues [25][26][27]. Consequently, fractional NLSE models have become essential for understanding soliton dynamics in optical fibers, with various solution schemes developed over the past two decades [28][29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

Mohammed,

Agarwal,

Brevik

et al. 2024

Symmetry

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Recently, nonlinear fractional models have become increasingly important for describing phenomena occurring in science and engineering fields, especially those including symmetric kernels. In the current article, we examine two reliable methods for solving fractional coupled nonlinear Schrödinger models. These methods are known as the Sardar-subequation technique (SSET) and the improved generalized tanh-function technique (IGTHFT). Numerous novel soliton solutions are computed using different formats, such as periodic, bell-shaped, dark, and combination single bright along with kink, periodic, and single soliton solutions. Additionally, single solitary wave, multi-wave, and periodic kink combined solutions are evaluated. The behavioral traits of the retrieved solutions are illustrated by certain distinctive two-dimensional, three-dimensional, and contour graphs. The results are encouraging, since they show that the suggested methods are trustworthy, consistent, and efficient in finding accurate solutions to the various challenging nonlinear problems that have recently surfaced in applied sciences, engineering, and nonlinear optics.

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“…Many researches (Kruskal, Zabusky, Miura, Gardner, Zakharov, Shabat, Zakharov, Mikhailov, Ablowitz, Newell, Segur, Kaup, Manakov, and other distinguished scientists) have been carried out in fields such as nonlinear wave dynamics, nonlinear optics, solid state, plasma, and quantum physics, atmosphere, ocean engineering and planetary sciences due to both the introduction of the soliton concept into the literature and the integrability of nonlinear equations and the development of computer-aided symbolic software. Especially in the last two decades, new concepts, theories, and models related to nonlinearity have been developed and most of them have been supported by experimental studies [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] . Due to the increase in studies on solitons, the orientation of many researchers to this field.…”

Section: Introductionmentioning

confidence: 99%

Obtaining the soliton solutions of local M-fractional magneto-electro-elastic media

Özdemir

Seçer

Özişik

et al. 2023

Heliyon

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Computational investigation on a nonlinear dispersion model with the weak non-local nonlinearity in quantum mechanics

Cited by 32 publications

References 28 publications

Optical soliton solutions of the perturbed fourth-order nonlinear Schrödinger-Hirota equation with parabolic law nonlinearity of self-phase modulation

Optical soliton solutions of the perturbed fourth-order nonlinear Schrödinger-Hirota equation with parabolic law nonlinearity of self-phase modulation

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

Obtaining the soliton solutions of local M-fractional magneto-electro-elastic media

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