Ion-acoustic wave structures in the fluid ions modeled by higher dimensional generalized Korteweg-de Vries–Zakharov–Kuznetsov equation

Younas, Usman; Ren, Jing; Baber, Muhammad Zafarullah; Yasin, Muhammad W.; Shahzad, Tahir

doi:10.1016/j.joes.2022.05.005

Cited by 24 publications

(15 citation statements)

References 59 publications

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“…The nonlinear ordinary differential equation observed in (13), is an approved equation to performing the balance principle between U ′′ and U 3 .…”

Section: Applications Of the Proposed Methodsmentioning

confidence: 99%

“…; Case 2. The following coefficients are the outcomes from solving the system (18) The parameters in (21) along with using ( 14) were substituted into (13), and the result was the following solution of (1):…”

Section: Application Of Erscm To the Aforementioned Modelmentioning

confidence: 99%

“…The parameters in (23) along with ( 14) were substituted into (13), and the outcomes are the following solution of (1):…”

Section: Application Of Erscm To the Aforementioned Modelmentioning

confidence: 99%

“…For solving the model stated in (1) through the use of the METM, firstly applying the balance principle in (13) between U ′′ and U 3 one immediately gets m = 1. Thereafter (7) becomes…”

Section: Application Of Metm To the Aforementioned Modelmentioning

confidence: 99%

“…The (3+1)-dimensional (gKdV-ZK) and its variations versions are important nonlinear models appearing in physics and engineering. Since then, the search for the solution of the gKdV-ZK equation and its variations were studied intensively with respect to different methods, such as using the Lie symmetry approach [12], the bilinear transformation-model and the expansion version of the φ 6 method [13], the new modification of the extended direct algebraic method [14], implementing of the fractional direct algebraic methods and the extended direct algebraic method, to present solitary wave solutions. Furthermore, the stability analysis is discussed [15], the extended F-expansion technique and the expansion version of the exp(−φ (F )) approach [16], the first integral method [17], through using Painlevé expansion, the Painlevé--Bäcklund transformations are obtained, and the bilinear forms of (1) have been derived [18].…”

Section: Introductionmentioning

confidence: 99%

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Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation

Mahmud¹,

Tanrıverdi²,

Muhamad³

et al. 2023

J. Appl. Math. Comput. Mech.

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The generalized Korteweg-de Varies-Zakharov-Kuznetsov equation (gKdV-ZK) in (3+1)-dimension has been investigated in this research. This model is used to elucidate how a magnetic field affects the weak ion-acoustic wave in the field of plasma physics.To deftly analyze the wide range of wave structures, we utilized the modified extended tanh and the extended rational sinh-cosh methods. Hyperbolic, periodic, and traveling wave solutions are presented as the results. Consequently, solitary wave solutions are also attained. This study shows that the solutions reported here are distinctive when our findings are contrasted against well-known outcomes. Moreover, realized findings are figured out in 3-dimensional, 2-dimensional, and contour profile graphs for the reader to comprehend their dynamics due to parameter selection. According to the findings, we can conclude that the suggested computational techniques are simple, dynamic, and well-organized. These methods are very functional for numerical calculations of complex nonlinear problems. Our results include a fundamental starting point in understanding physical behavior and the structure of the studied systems.

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“…The nonlinear ordinary differential equation observed in (13), is an approved equation to performing the balance principle between U ′′ and U 3 .…”

Section: Applications Of the Proposed Methodsmentioning

confidence: 99%

Section: Application Of Erscm To the Aforementioned Modelmentioning

confidence: 99%

“…The parameters in (23) along with ( 14) were substituted into (13), and the outcomes are the following solution of (1):…”

Section: Application Of Erscm To the Aforementioned Modelmentioning

confidence: 99%

“…For solving the model stated in (1) through the use of the METM, firstly applying the balance principle in (13) between U ′′ and U 3 one immediately gets m = 1. Thereafter (7) becomes…”

Section: Application Of Metm To the Aforementioned Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation

Mahmud¹,

Tanrıverdi²,

Muhamad³

et al. 2023

J. Appl. Math. Comput. Mech.

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Breather, lump, M-shape and other interaction for the Poisson–Nernst–Planck equation in biological membranes

Ceesay,

Ahmed,

Baber

et al. 2024

Opt Quant Electron

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This paper investigates a novel method for exploring soliton behavior in ion transport across biological membranes. This study uses the Hirota bilinear transformation technique together with the Poisson–Nernst–Planck equation. A thorough grasp of ion transport dynamics is crucial in many different scientific fields since biological membranes are important in controlling the movement of ions within cells. By extending the standard equation, the suggested methodology offers a more thorough framework for examining ion transport processes. We examine a variety of ion-acoustic wave structures using the Hirota bilinear transformation technique. The different forms of solitons are obtained including breather waves, lump waves, mixed-type waves, periodic cross-kink waves, M-shaped rational waves, M-shaped rational wave solutions with one kink, and M-shaped rational waves with two kinks. It is evident from these numerous wave shapes that ion transport inside biological membranes is highly relevant, and they provide important insights that may have an impact on various scientific disciplines, medication development, and other areas. This extensive approach helps scholars dig deeper into the complexity of ion transport, illuminating the complicated mechanisms driving this essential biological function. Additionally, to show the physical interpretations of these solutions we construct the 3D and their corresponding contour plots by choosing the different values of constants. So, these solutions give us the better physical behaviors.

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Unraveling the dynamic complexity: exploring the (3+1)-dimensional conformable mKdV-ZK equation

Ding,

Boulaaras,

Rehman

et al. 2024

Opt Quant Electron

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Ion-acoustic wave structures in the fluid ions modeled by higher dimensional generalized Korteweg-de Vries–Zakharov–Kuznetsov equation

Cited by 24 publications

References 59 publications

Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation

Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation

Breather, lump, M-shape and other interaction for the Poisson–Nernst–Planck equation in biological membranes

Unraveling the dynamic complexity: exploring the (3+1)-dimensional conformable mKdV-ZK equation

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