Sub-10-fs-pulse propagation between analytical and numerical investigation

Khater, Mostafa M. A.; Elagan, S. K.; Mousa, Abd Allah A.; El-Shorbagy, M. A.; Alfalqi, Suleman H.; Alzaidi, Jameel F.; Lu, Dianchen

doi:10.1016/j.rinp.2021.104133

Cited by 45 publications

(3 citation statements)

References 38 publications

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“…It is also helpful in problem of optical pulse propagation in asymmetric, twin core optical fibers etc. Optical solitons, which are one of the most important solutions of nonlinear Schrodinger equation, are used in optical fiber communication [ 44 , 48 , 64 , 65 , 66 , 67 , 68 , 69 ].…”

Section: Nonlinear Evolutionary Equations and Their Examplesmentioning

confidence: 99%

Soliton: A dispersion-less solution with existence and its types

Arora

Rani

Emadifar

2022

Heliyon

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Section: Nonlinear Evolutionary Equations and Their Examplesmentioning

confidence: 99%

Soliton: A dispersion-less solution with existence and its types

Arora

Rani

Emadifar

2022

Heliyon

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“…Numerous researchers have developed different methods and approaches to examine analytical solutions considering the significance of these models and their varied applications. The F-expansion approach [ 1 ], Lie symmetry technique [ 2 ], Kudryashov process [ 3 ], -expansion technique [ 4 ], rational sine–cosine scheme [ 5 ], modified Jacobi elliptic expansion method [ 6 ], exponential-expansion scheme [ 7 ], generalized exponential method [ 8 ], the hyperbolic function method [ 9 ], positive quadratic function method [ 10 ], the inverse scattering approach [ 11 ], generalized Khater technique [ 12 ], test function method [ 13 ], improved tanh method [ 14 ], different form of the -expansion methods [ 15 – 18 ], and other such methods are examples of these approaches.…”

Section: Introductionmentioning

confidence: 99%

On traveling wave solutions with stability and phase plane analysis for the modified Benjamin-Bona-Mahony equation

Sagib,

Hossain,

Saha

et al. 2024

PLoS ONE

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The modified Benjamin-Bona-Mahony (mBBM) model is utilized in the optical illusion field to describe the propagation of long waves in a nonlinear dispersive medium during a visual illusion (Khater 2021). This article investigates the mBBM equation through the utilization of the rational ( G ′ G )-expansion technique to derive new analytical wave solutions. The analytical solutions we have obtained comprise hyperbolic, trigonometric, and rational functions. Some of these exact solutions closely align with previously published results in specific cases, affirming the validity of our other solutions. To provide insights into diverse wave propagation characteristics, we have conducted an in-depth analysis of these solutions using 2D, 3D, and density plots. We also investigated the effects of various parameters on the characteristics of the obtained wave solutions of the model. Moreover, we employed the techniques of linear stability to perform stability analysis of the considered model. Additionally, we have explored the stability of the associated dynamical system through the application of phase plane theory. This study also demonstrates the efficacy and capabilities of the rational ( G ′ G )-expansion approach in analyzing and extracting soliton solutions from nonlinear partial differential equations.

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“…Khater et al [26] investigated the analytical and semi-analytical solutions of the time-fractional Cahn-Allen equation by using the Adomian decomposition method. Khater et al [27] found the analytical solutions of the nonlinear Schrodinger equation with the higher-order through Kudryashov method. They also found the solutions of quadratic cubic fractional nonlinear Schrodinger equation by Adomian decomposition process [28].…”

Section: Introductionmentioning

confidence: 99%

Efficient Numerical Scheme for the Solution of HIV Infection CD4+ T-Cells Using Haar Wavelet Technique

Amin¹,

Yüzbaşı²,

Nazir³

2022

Computer Modeling in Engineering &Amp; Sciences

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In this paper, Haar collocation algorithm is developed for the solution of first-order of HIV infection CD4 + T-Cells model. In this technique, the derivative in the nonlinear model is approximated by utilizing Haar functions. The value of the unknown function is obtained by the process of integration. Error estimation is also discussed, which aims to reduce the error of numerical solutions. The numerical results show that the method is simply applicable. The results are compared with Runge-Kutta technique, Bessel collocation technique, LADM-Pade and Galerkin technique available in the literature. The results show that the Haar technique is easy, precise and effective.

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Sub-10-fs-pulse propagation between analytical and numerical investigation

Cited by 45 publications

References 38 publications

Soliton: A dispersion-less solution with existence and its types

Soliton: A dispersion-less solution with existence and its types

On traveling wave solutions with stability and phase plane analysis for the modified Benjamin-Bona-Mahony equation

Efficient Numerical Scheme for the Solution of HIV Infection CD4+ T-Cells Using Haar Wavelet Technique

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