Optical solitons with modified extended direct algebraic method for quadratic-cubic nonlinearity

Hubert, Malwe Boudoue; Justin, Mibaile; Betchewe, Gambo; Doka, Serge Y.; Biswas, Anjan; Zhou, Qin; Ekici, Mehmet; Moshokoa, Seithuti P.; Belić, Milivoj R.

doi:10.1016/j.ijleo.2018.02.074

Cited by 41 publications

(5 citation statements)

References 11 publications

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“…( 5) into Eq. ( 30), and applying (Hubert et al 2018), then, the solutions of Eqs. ( 6) and ( 7) can be represented as:…”

Section: Travel Wave Solutions For a System Coupled Of Nlsementioning

confidence: 99%

“…where y( ) is a Jacobian elliptic function (see Hubert et al 2018;Arshad et al 2017), which can be represented as follows:…”

Section: Travel Wave Solutions For a System Coupled Of Nlsementioning

confidence: 99%

“…The exact solutions of the nonlinear partial differential equation (NLPDE) play an important role in the nonlinear problems, a number of method have been developed, such as Kudryashov's method, Generalized Jacobi's elliptic function expansion, extended trial equation method, P 6 model approach, Bernoulli's equation method, first integral technique and modified extended direct algebraic method (Mirzazadeh et al 2018;Zayed et al 2020a, b, c;Ekici et al 2017a, b;Zhou et al 2015;Mirzazadeh et al 2015;Biswas et al 2014;Hubert et al 2018;Dieu-donne et al 2020). The modified extended direct algebraic method have been suggested to obtain the exact complex solutions of nonlinear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Ahmed

Rabie

2021

Opt Quant Electron

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In this paper, we apply modified extended direct algebraic method to obtain optical soliton solutions in magneto-optic waveguides with dual-power law nonlinearity. Dark, bright, singular, bright-dark combo and singular-bright combo soliton solutions are obtained. Also, periodic solutions and Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, 3D and 2D graphs are presented.

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“…( 5) into Eq. ( 30), and applying (Hubert et al 2018), then, the solutions of Eqs. ( 6) and ( 7) can be represented as:…”

Section: Travel Wave Solutions For a System Coupled Of Nlsementioning

confidence: 99%

“…where y( ) is a Jacobian elliptic function (see Hubert et al 2018;Arshad et al 2017), which can be represented as follows:…”

Section: Travel Wave Solutions For a System Coupled Of Nlsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Ahmed

Rabie

2021

Opt Quant Electron

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“…Recently many powerful techniques for attaining the exact solution of NPDEs have been presented, such as Jacobi-elliptic approach 7 , Sine-Gordon expansion scheme 8 – 10 , modified simple equation scheme 11 , the Kudryashov approach 12 , auxiliary equation technique 13 , 14 , Exp-function method 15 , the extended direct algebraic method 16 – 19 , -expansion method 17 , 20 , extended tanh expansion scheme 21 , -expansion method 22 , Hirota bilinear method 23 , 24 , modified rational expansion method 25 , modified Sardar sub-equation method 26 , the Riccati equation mapping method 27 , F-expansion method 28 and many more 29 – 33 .…”

Section: Introductionmentioning

confidence: 99%

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

Shakeel,

Zafar,

Alameri

et al. 2024

Sci Rep

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This work examines the fractional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) by utilizing three well-known analytical methods, the modified $$\left( \frac{G^{'}}{G^2}\right)$$ G ′ G 2 -expansion method, $$\left( \frac{1}{G^{'}}\right)$$ 1 G ′ -expansion method and the Kudryashov method. The gKdV-ZK equation is a nonlinear model describing the influence of magnetic field on weak ion-acoustic waves in plasma made up of cool and hot electrons. The kink, singular, anti-kink, periodic, and bright soliton solutions are observed. The effect of the fractional parameter on wave shapes have been analyzed by displaying various graphs for fractional-order values of $$\beta$$ β . In addition, we utilize the Hamiltonian property to observe the stability of the attained solution and Galilean transformation for sensitivity analysis. The suggested methods can also be utilized to evaluate the nonlinear models that are being developed in a variety of scientific and technological fields, such as plasma physics. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complex models.

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“…Precise protracted predictions are unattainable with the existing technologies owing to this nonlinearity [4,5,6]. Various analytical methods have been utilized to solve different kinds of nonlinear equations, such as the extended direct algebraic method [7], the extended trial function method [8,9], the inverse scattering method [10], the Kudryashov expansion and sine-cosine method [11], the Jacobi elliptic function [12,13,14], modified generalized exponential rational function [15] and many others [16,17,18,19,20,21,22,23,24,25,26,27,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Optical solitons to the Perturbed Gerdjikov-Ivanov equation with quantic nonlinearity

et al. 2023

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In this article, we examine the Perturbed Gerdjikov-Ivanov equation by using the Jacobi elliptic function expansion method. This results in obtaining distinct solutions including dark, bright, singular solitons, periodic waves, singular periodic waves, and Jacobi elliptic function solutions. The 2-and 3-dimensional graphs of the reported solutions are presented. The reported results may be useful in explaining the physical features of the studied equation.

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Optical solitons with modified extended direct algebraic method for quadratic-cubic nonlinearity

Cited by 41 publications

References 11 publications

Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

Optical solitons to the Perturbed Gerdjikov-Ivanov equation with quantic nonlinearity

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