Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

In this manuscript, the computational solutions of the nonlinear Klein-Gordon-Zakharov (KGZ) model are scrutinized through a new generalized analytical scheme. This mathematical model describes the evolution of strong Langmuir turbulence in plasma physics. Many distinctive solutions are obtained, such as linear, rational, hyperbolic, parabolic, and so on. 2D, 3D, contour, stream plots are plotted to demonstrate further physical and dynamical attitudes of the investigated model. The power, usefulness, and accuracy of the compensated schemes are revealed and tested. The capabilities for managing a class of nonlinear evolution equations of the new generalized method is assessed. Moreover, the stability property of the obtained solutions is checked by using the Hamiltonian system's characteristics.

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“…Employing the GKM through the homogeneous balance principles on Eq. (3), yield the following general solutions [44]…”

Section: Applicationsmentioning

confidence: 99%

Abundant novel wave solutions of nonlinear Klein–Gordon–Zakharov (KGZ) model

et al. 2021

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“…Shakeri and Dehghan [45] and Sakar et al [46] studied fractional partial differential equations using the homotopy perturbation method. Many researchers [47][48][49][50] have developed different techniques for solving fractional problems under various applied phenomena.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Time-Fractional Equivalent Width Equations That Describe Hydromagnetic Waves

2021

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The present research article is related to the analytical investigation of some fractional-order equal-width equations. The homotopy perturbation technique along with Elzaki transformation is implemented to discuss the fractional view analysis of equal-width equations. For better understanding of the proposed procedure some examples related to equal-width equations are presented. The identical behavior of the derived and actual solutions is observed. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences.

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“…Ganji and Rafei (2006) utilized the homotopy perturbation approach for investigating the exact solutions of system (2). For more details about other methods used to solve system (2), we refer to (Abdel-Aty et al, 2020a;Abdel-Aty et al, 2020b;Assas, 2008;Ali, Khan, Khater, Mousa, & Attia, 2021;Chu, Khater, & Hamed, 2021;Gokdogan, Yildirim, & Merdan, 2012;Jaradat, Syam, & Alquran, 2017;Khater, Attia, Park, & Lu, 2020;Khater, Attia, Alodhaibi, & Lu, 2020;Khater, Lu, Attia, & Inc, 2019;Qian, Attia, Qiu, Lu, & Khater, 2019;Yue, Khater, Inc, Attia, & Lu, 2020).…”

Section: Introductionmentioning

confidence: 99%

New exact and numerical solutions for the KdV system arising in physical applications

Almatrafi

Alharbi

Abdelrahman

2021

Arab Journal of Basic and Applied Sciences

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The Kortweg-de Vries (KdV) equation is more appropriate to simulate some natural phenomena and gives more accurate results for some physical systems such as the movement of water waves. In this work, novel analytical traveling wave solutions for a nonlinear KdV system are explored using the sech method. The exact solutions are presented in the form of hyperbolic functions. These solutions show the propagation of water waves on the surface. We also implement the numerical adaptive moving technique (MMPDEs) to construct the relevant system's numerical solutions. A detailed comparison between the numerical and analytical solutions is also presented to confirm the accuracy of the numerical technique. We present some new 2D and 3D figures to illustrate the behaviour of the exact and numerical solutions. The obtained numerical solutions verify the accuracy of the considered methods qualitatively and quantitatively. The stability of the obtained solutions is investigated using the Hamiltonian system. The achieved results can be applied for some new observations in the ocean, coastal water, macroscopic phenomena, and processes. The proposed techniques are potent tools to solve many other non-linear partial differential equations in applied mathematics.

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Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

Cited by 31 publications

References 61 publications

Abundant novel wave solutions of nonlinear Klein–Gordon–Zakharov (KGZ) model

Abundant novel wave solutions of nonlinear Klein–Gordon–Zakharov (KGZ) model

Numerical Investigation of Time-Fractional Equivalent Width Equations That Describe Hydromagnetic Waves

New exact and numerical solutions for the KdV system arising in physical applications

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