New kink solutions for the van der Waals p‐system

Az-Zo’bi, Emad A.

doi:10.1002/mma.5717

Cited by 20 publications

(2 citation statements)

References 39 publications

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“…The modified simple equation scheme has been successfully employed to analytically treat the Fitzhugh-Nagumo and Sharma-Tasso-Olver equations [33], the dimensionless modified KdV and reaction-diffusion equations [34], generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahon and non-commutative Burger equations [35], the van der Waals p-system [36], the higher dimensional Fokas equation [37], the nonlinear Klein-Gordon-Zakharov, generalized Davey-Stewartson, Davey-Stewartson, and generalized Zakharov equations [38], the nonlocal Ito integro-differential equation [39], some nonlinear Schrödinger-type equations [40,41], the shallow-water waves equation [42], the higher dimensional Calogero-Bogoyavlenskii-Schiff and Jimbo-Miwa equations [43], and the modified Fornberg-Whitham equation [44].…”

Section: Outline Of the Methodologymentioning

confidence: 99%

Assorted Spatial Optical Dynamics of a Generalized Fractional Quadruple Nematic Liquid Crystal System in Non-Local Media

Al Zubi,

Afef,

Az-Zo’bi

2024

Symmetry

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Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The expanded MSEM is investigated to enlarge the applicability of the standard one. The suggested expansion depends on merging the MSEM and the ansatz method. The new generalized nonlinear n-times quadruple power law is included. With the aid of the symbolic computational package Mathematica, new explicit complex hyperbolic, periodic, and more exact spatial soliton solutions are derived. Moreover, the related existence constraints are obtained. To show the dynamical properties of some of the obtained nematicons, three-dimensional profiles with corresponding contours are depicted with the choice of appropriate values of arbitrary parameters. The fractional impacts in various applicable senses are analyzed to investigate the generality of the considered model.

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Section: Outline Of the Methodologymentioning

confidence: 99%

Assorted Spatial Optical Dynamics of a Generalized Fractional Quadruple Nematic Liquid Crystal System in Non-Local Media

Al Zubi,

Afef,

Az-Zo’bi

2024

Symmetry

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“…The MSEM and its various extensions are successfully implemented to tackle a wide range of NLEEs and systems. For the most recent related works, we mention the Ito integrodifferential equation [42], fiber Bragg grating model [43], weakly nonlocal Schrödinger equation with parabolic nonlinearity [44], modified Camassa-Holm equation [45], Lakshmanan-Porsezian-Daniel model [46], van der Waals p-system [47], Kundu-Mukherjee-Naskar model [48], modified Fornberg-Whitham equation [49], Kundu-Eckhaus equation and derivative nonlinear Schrodinger equation [50], Landau-Ginzburg-Higgs equation, and Cahn-Allen equation [51].…”

Section: Methodsmentioning

confidence: 99%

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

et al. 2021

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This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed for this purpose under some parametric constraints. The computational work shows the difference, effectiveness, reliability, and power of the considered scheme. This method can treat several complex higher-order NLSEs that arise in mathematical physics. Graphical illustrations of some obtained solitons are presented.

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Sensitivity and wave propagation analysis of the time-fractional (3+1)-dimensional shallow water waves model

Şenol,

Gençyiğit,

Demirbilek

et al. 2024

Z. Angew. Math. Phys.

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This study investigates the exact solutions of the time-fractional (3+1)-dimensional combined Korteweg–de Vries Benjamin–Bona–Mahony (KdV-BBM) equation. The considered model describes the long surface gravity waves of small amplitude, which portrays the two-way propagation of waves. The modified generalized Kudryashov method and the exp(-$$\varphi (\xi $$ φ ( ξ ))-expansion methods are employed to resolve the aforementioned issue because of their effectiveness and simplicity. For generality, the time fractional version is studied; more advanced solutions that do not exist in the literature were obtained. As a result, a variety of the exact wave solutions of the conformable (3+1)-dimensional KdV-BBM equation are obtained. The dynamical behaviors of some obtained solutions are represented with the proper parameter values. The used methods yield noteworthy results in obtaining the analytical solutions of fractional differential equations under various conditions. Besides, the sensitivity of regarding dynamical system is assessed to show the numerical stability effects.

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New kink solutions for the van der Waals p‐system

Cited by 20 publications

References 39 publications

Assorted Spatial Optical Dynamics of a Generalized Fractional Quadruple Nematic Liquid Crystal System in Non-Local Media

Assorted Spatial Optical Dynamics of a Generalized Fractional Quadruple Nematic Liquid Crystal System in Non-Local Media

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

Sensitivity and wave propagation analysis of the time-fractional (3+1)-dimensional shallow water waves model

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