Homotopy perturbation and Adomian decomposition methods for modeling the nonplanar structures in a bi-ion ionospheric superthermal plasma

El-Tantawy, S. A.; Shan, S. Ali; Mustafa, Naeem; Alshehri, Mansoor H.; Duraihem, Faisal Z.; Turki, Nasser Bin

doi:10.1140/epjp/s13360-021-01494-w

Cited by 18 publications

(2 citation statements)

References 57 publications

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“…The future work could include physical effects like collisional force between the particles inside the plasma or nonplanar geometrical effects which make the resulting nonlinear evolution equations nonintegrable. [65][66][67] For solving and analyzing these evolution equations, some approximate techniques such as the family of the homotopy perturbation method (HPM), 68,69 the family of Adomian decomposition method (ADM), 70 and many other numerical methods 71 could be gainfully employed.…”

Section: Discussionmentioning

confidence: 99%

Overtaking interaction of electron-acoustic solitons in Saturn’s magnetosphere

Khattak

Masood

Jahangir

et al. 2023

Journal of Low Frequency Noise, Vibration and Active Control

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The progression of nonlinear electron-acoustic waves (EAWs) in a magnetized and collision-free plasma made up of cold inertial electrons, inertialess superthermal electrons, and stationary background ions with special reference to Saturn’s magnetosphere (SMS) is explored. The method of reductive perturbation (MRP) is employed to obtain the evolution equation (i.e., Zakharov– Kuznetsov equation (ZKE)) that governs the propagation of electron acoustic solitons (EASs). Using the elegant and efficient Hirota bilinear method (HBM), multi-soliton solutions (MSSs) of the ZKE are determined. The impact of the effects of hot-to-cold electron density ratio, magnetic field (MF) strength, and superthermality on single as well as the interaction of EASs is examined. Estimates of the values of the electric field at several radii of SMS (i.e., 12 R s − 17.8 R s, where R s is the radius of Saturn) are presented, which are found in μV/ m to mV/ m range and are in perfect agreement with the data from Cassini radio and plasma wave science wideband receiver. Moreover, the influence of the relevant plasma parameters on the interaction time and spatial extent of the interacting EASs is also explored.

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Section: Discussionmentioning

confidence: 99%

Overtaking interaction of electron-acoustic solitons in Saturn’s magnetosphere

Khattak

Masood

Jahangir

et al. 2023

Journal of Low Frequency Noise, Vibration and Active Control

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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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