The phase shift analysis of the colliding dissipative KdV solitons

Albalawi, Wedad; El-Tantawy, S. A.; Alkhateeb, Sadah A.

doi:10.1016/j.joes.2021.09.021

Cited by 31 publications

(6 citation statements)

References 51 publications

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“…Finally, the proposed methods can be used to interpret and analyze many nonlinear phenomena that arises in plasma physics, such as soliton waves, rogue waves, shock waves, etc. [10][11][12][13][14][15][16][17][18][19]. Data Availability Statement: Data sharing is not applicable to this article as no new data were created or analyzed in this study.…”

Section: Discussionmentioning

confidence: 99%

“…Partial differential equations (PDEs) are mathematical equations that described physical processes involving multiple independent variables, such as time and space. They play a crucial role in modeling many phenomena in science and engineering, including fluid dynamics, electromagnetism, quantum mechanics, and plasma physics [10][11][12][13][14][15][16][17][18][19]. The important area of partial differential equations is the fractional system of PDEs, which extends the traditional integer-order calculus to non-integer orders [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

et al. 2023

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In this article, we present a modified strategy that combines the residual power series method with the Laplace transformation and a novel iterative technique for generating a series solution to the fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use the Laurent series in their development. The new procedures’ advantages include the accuracy and speed in obtaining exact/approximate solutions. The suggested approach examines the fractional nonlinear BZ system that describes flow motion in a pipe.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

et al. 2023

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“…This type of localized wave was discussed and interpreted by studies of numerical simulation of the Korteweg-de Vries (KdV) equation. 7 Washimi and Taniuti 8 explored the ion-acoustic (IA) solitons theoretically by using the reductive perturbation technique (RPT) to derive the KdVequation while the experimental proof of the soliton was carried out by Ikezi et al 9 Many researchers illustrated the dynamics of SWs that can exist and propagate in several mediums in the frame of the KdV equation [10][11][12] and its family of third-order dispersion such as a modified KdV (mKdV) equation with cubic nonlinearity, 13,14 Schamel KdVequation with fractal nonlinearity, 15,16 extended KdVequation with quadratic and cubic nonlinearities, and so on. 1,2 On the other side, there is another family for the KdV equation but with fifth-order dispersion, known as Kawaharatype equations.…”

Section: Introductionmentioning

confidence: 99%

Nonplanar ion-acoustic solitary and cnoidal waves in a non-Maxwellian plasma: Study on nonplanar (modified) Kawahara equation

Almutlak,

Khalid,

El-Tantawy

2023

Journal of Low Frequency Noise, Vibration and Active Control

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This study aims to examine the properties of the nonplanar (cylindrical and spherical) ion-acoustic solitary waves (SWs) and cnoidal waves (CWs) in a collisionless, unmagnetized electron-ion (EI) plasma having a Cairns–Tsallis distribution for the electrons. This study is structured around two main lines. The first trend involves deriving the nonplanar Korteweg-de Vries (KdV) equation by utilizing the method of reductive perturbation (MRP). This equation describes small-amplitude (non)planar acoustic waves (AWs). Furthermore, the nonplanar Kawahara equation (KE) is formulated to examine the significant magnitude of planar and nonplanar SWs and CWs. The current plasma model supports compressive and rarefactive IA solitary and cnoidal structures, depending upon the associated physical factors such as the nonextensive parameter (nonextensivity) and nonthermal parameter (nonthermality). When the plasma compositions reach some critical values, such as the critical value of nonthermality, the coefficient of the quadratic nonlinear term vanishes. Hence, both nonplanar modified KdV (mKdV) equation and modified KE (mKE) with cubic nonlinearity are derived to accurately depict the dynamics of both small and large amplitudes of nonplanar SWs and CWs and any other structures related to this family of evolution equations. The influences of the nonextensivity and nonthermality on the profile of (non)planar KdV soliton and the (non)planar Kawahara SWs and CWs are numerically examined using some semi-analytical and numerical approximations. Also, the impact of the nonextensivity on the profile of (non)planar mKdV soliton and the (non)planar modified Kawahara SWs and CWs is reported. It is tracked down that the variety of different plasma parameters significantly alters the characteristic properties of the small and large amplitude ion-acoustic waves (IAWs) discussed by the nonplanar KdV-type equations.

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“…The exact result of such nonlinear phenomena may not be possible for some physical problems. For instance in a plasma physics, there are many nonintegrable PDEs that can not support exact analytic solutions such as the integer and fractional damped thirdorder KdV-type equations and the damped integer and fractional fifth-order KdV-type equations (the family of damped Kawahara equation) and many other equations related to plasma physics [35][36][37][38][39][40]. Moreover, in non-Maxwellian plasma models that have trapped particles follow nonisothermal or Schamel distribution in addition to the particle kinematic viscosity, in this case, the fluid equations of the plasma model can be reduced to a nonintegrable damped Schamel KdV-Burgers equation [41,42].…”

Section: Introductionmentioning

confidence: 99%

Study of Fuzzy Fractional Third-Order Dispersive KdV Equation in a Plasma under Atangana-Baleanu Derivative

Areshi

El-Tantawy

Alotaibi

et al. 2022

Journal of Function Spaces

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Motivated by the wide-spread of both integer and fractional third-order dispersive Korteweg-de Vries (KdV) equations in explaining many nonlinear phenomena in a plasma and many other fluid models, thus, in this article, we constructed a system for calculating an analytical solution to a fractional fuzzy third-order dispersive KdV problems. We implemented the Shehu transformation and the iterative transformation technique under the Atangana-Baleanu fractional derivative. The achieved series result was contacted and determined the analytic value of the suggested models. For the confirmation of our system, three various problems have been represented, and the fuzzy type solution was determined. The fuzzy results of upper and lower section of all three problems are simulate applying two different fractional orders among zero and one. Because it globalises the dynamic properties of the specified equation, it delivers all forms of fuzzy solutions occurring at any fractional order among zero and one. The present results can help many researchers to explain the nonlinear phenomena that can create and propagate in several plasma models.

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The phase shift analysis of the colliding dissipative KdV solitons

Cited by 31 publications

References 51 publications

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

Nonplanar ion-acoustic solitary and cnoidal waves in a non-Maxwellian plasma: Study on nonplanar (modified) Kawahara equation

Study of Fuzzy Fractional Third-Order Dispersive KdV Equation in a Plasma under Atangana-Baleanu Derivative

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