Effect of trapped electron on the dust ion acoustic waves in dusty plasma using time fractional modified Korteweg-de Vries equation

Nazari-Golshan, Akbar; Nourazar, S. Salman

doi:10.1063/1.4823997

Cited by 22 publications

(9 citation statements)

References 40 publications

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“…These parameters are employed to control the center of the rogue waves. The dynamic behaviors of generalized high-order rogue wave solutions with a controllable center of the 3D KDV-BBM equation are shown in some three-dimensions and contour plots [see figures [4][5][6]. The novel dynamics of the 9-rogue wave has not been reported in [45][46][47][48] using the same method.…”

Section: Discussionmentioning

confidence: 99%

“…This is a milestone in soliton theory. Since then, the research of soliton in various fields has developed rapidly, such as nonlinear optics, condensed matter, fluid mechanics, plasma physics, acoustic wave propagation, etc [3][4][5][6][7][8]. The exact solutions have been well studied in (1+1)-dimensional [1D] [9][10][11][12] and (2+1)-dimensional [2D] systems [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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On constructing of multiple rogue wave solutions to the (3+1)-dimensional Korteweg–de Vries Benjamin-Bona-Mahony equation

Cao¹,

Tian

Ghanbari

2021

Phys. Scr.

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Exploring new wave soliton solutions to nonlinear partial differential equations has always been one of the most challenging issues in different branches of science, including physics, applied mathematics and engineering. In this paper, we construct multiple rogue waves of (3+1)-dimensional Korteweg–de Vries Benjamin-Bona-Mahony equation through a symbolic calculation approach. Further, a detailed analysis of the localization features of first-order rogue wave solution is also presented. We discuss the influence of the parameters in the equation on the localization and characteristics of a rogue wave, as well as the control of their amplitude, depth, and width. In order to achieve these desired results, a series of polynomial functions are utilized to construct the generalized multiple rogue waves with a controllable center. Based on the bilinear form of this equation, 3-rogue wave solutions, 6-rogue wave solutions, and 9-rogue wave solutions are generated, respectively. The 3-rogue wave has a ‘triangle-shaped’ structure. The center of the 6-rogue wave forms a circle around a single rogue wave. The 9-rogue wave consists of seven first-order rogue waves and one second-order rogue waves as the center. Taking some appropriate parameters into account, their complex and interesting dynamics are shown in three-dimensional and contour plots. These new results are useful to understand the new features of nonlinear dynamics in real-world applications.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On constructing of multiple rogue wave solutions to the (3+1)-dimensional Korteweg–de Vries Benjamin-Bona-Mahony equation

Cao¹,

Tian

Ghanbari

2021

Phys. Scr.

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“…For a frame moving with a speed U and V the soliton solution of equation (47) the solution of set of equations (47) in a planner geometry is given by…”

Section: The Phase Shifts Of Ion Acoustic Shock Wavesmentioning

confidence: 99%

“…In comparing the solitary and shocks solutions with observation data [40][41][42][43][44] it was recovered that the amplitude of solitons and shocks would underestimate in a range of 20% [45,46]. To reduce this variation in the amplitude, different methods have been proposed such as algebraic techniques, higher order approximations, and time fractional solution of the nonlinear PDEs [47,48]. Albuohimad et al applied spectral collection method to find the numerical solution of time-fractional coupled KdV equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution and characteristic study of time-fractional shocks collision

Shakeel¹,

Parveen²,

Islam³

et al. 2021

Phys. Scr.

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In this study, the interaction of counter-propagating ion acoustic shock waves in three-component unmagnetized plasmas with inertial warm ions, superthermal electrons and positrons are examined. By employing the extended Poincare-Lighthill-Kuo (PLK) method, two-sided Korteweg-deVries-Burgers (KdVB) equations and their corresponding phase shifts for the shock wave are also derived. The derived two-sided KdVB equations are converted to two-sided time-fractional KdVB (TFKdVB) equations by semi inverse method, which is then solved numerically by a local meshless method (LMM). The effects of the ratio of electron temperature to positron temperature, the spectral index κ e , κ p and fractional concentration of positron component p on the phase shift are also examined. Figures are given to judge the performance of the LMM. Comparison is made with the exact solution for the classical case (i.e. ρ = 1) and with Petrov-Galerkin method (PGM) in case of fractional derivative. The influence of the fractional parameter on the behaviour of ion acoustic shock wave in e-p-i plasma is investigated.

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“…[16] Effects of trapped hot electrons on acoustic soliton have been discussed by using the mKdV equation with time fractional term. [17] Guo et al studied the progress of ionic waves in ion pair plasmas model via the Gardner equation with the time fraction term. They used the method of variational iteration to investigate the nonthermal electrons' effect on the produced wave.…”

mentioning

confidence: 99%