The New Wave Structures to the Fractional Ion Sound and Langmuir Waves Equation in Plasma Physics

Abdelrahman, Mahmoud A. E.; Hassan, S. Z.; Alomair, R. A.; Al-Saleh, Dana

doi:10.3390/fractalfract6050227

Cited by 10 publications

(3 citation statements)

References 53 publications

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“…In addition, applications of fractional differential equations to ISLW models are described in Ref. [42] , [43] . In future studies, we need to develop the fractional differential equation of this model by the unified method.…”

Section: Discussionmentioning

confidence: 99%

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Application of the unified method to solve the ion sound and Langmuir waves model

Nandi

Roshid

Ali

2022

Heliyon

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Section: Discussionmentioning

confidence: 99%

“…The fractional ISLW model is studied in ref. [42] , [43] , and the fractional generalized HSC KdV model is studied in ref. [44] .…”

Section: Introductionmentioning

confidence: 99%

Application of the unified method to solve the ion sound and Langmuir waves model

Nandi

Roshid

Ali

2022

Heliyon

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“…In recent years, mathematicians and physicists have become more interested in the exploration of complex wave propagation characterized by a certain type of nonlinear fractional partial diferential equations (NFPDEs) [1][2][3][4]. Tese equations play an important role in describing the dynamical processes and physical phenomena in plasma physics, superconductivity, chemical engineering, biochemistry, ocean engineering, networked systems, fber communications, industrial studies, and many other scientifc felds [5][6][7]. As a result, it is crucial to investigate the exact wave solutions to NFPDEs when looking at nonlinear physical occurrences.…”

Section: Introductionmentioning

confidence: 99%

Novel Explosive and Super Fractional Nonlinear Schrödinger Structures

Abdelwahed,

Alsarhan,

El-Shewy

et al. 2023

Journal of Mathematics

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The fractional nonlinear Schrödinger equation solutions have been investigated via fraction space-time derivative sense. We applied the unified technique for this model to extract new structures of waves. The fractional property structures were obtained from the model in form of hyperbolic, soliton, shock, explosive, superperiodic, and trigonometric structures. It was found that increasing fractal factors produces a change in the phase and wave frequency of propagating nonlinear waves. The physical models that explain tidal energy generation are crucial to the development of contemporary green power systems. The parametric description for wave characteristics in this process is created by the solution of nonlinear equations. The obtained solutions are applicable in new communications, energy applications, fractional quantum modes, and in science and complex phenomena in astrophysics. Finally, the proposed technique can be implemented for further fractional physical models.

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Bifurcation, quasi‐periodic, chaotic pattern, and soliton solutions for a time‐fractional dynamical system of ion sound and Langmuir waves

Elmandouh

2024

Math Methods in App Sciences

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This paper strives to investigate the time fractional system that characterizes the ion sound wave influenced by the ponderomotive force induced by a high‐frequency field, as well as the Langmuir wave in plasma. Initially, based on the qualitative theory for planar integrable systems, four‐phase portraits are found in the phase plane under certain conditions on the physical parameters. These conditions are used to prove analytically the existence of solitary, kink (anti‐kink), periodic, super‐periodic, and unbounded wave solutions. The correspondence between the energy levels, phase orbits, and consequently the type of the solution is announced. We derived the bounded wave solutions associated with the phase orbits, which are shown to be consistent with the qualitative analysis of the types of solutions. Moreover, we studied the consistency between the obtained solutions by investigating the degeneracy of the solutions through the transmission between the phase orbits, or equivalently, through the dependence on the initial conditions. With the presence of perturbed periodic terms, the quasi‐periodic behavior and chaotic patterns are investigated.

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The New Wave Structures to the Fractional Ion Sound and Langmuir Waves Equation in Plasma Physics

Cited by 10 publications

References 53 publications

Application of the unified method to solve the ion sound and Langmuir waves model

Application of the unified method to solve the ion sound and Langmuir waves model

Novel Explosive and Super Fractional Nonlinear Schrödinger Structures

Bifurcation, quasi‐periodic, chaotic pattern, and soliton solutions for a time‐fractional dynamical system of ion sound and Langmuir waves

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