Numerical simulations of Zakharov’s (ZK) non-dimensional equation arising in Langmuir and ion-acoustic waves

2021 ◽  
pp. 2150480
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Acoustic Waves ◽  
Electromagnetic Waves ◽  
Low Frequency ◽  
Expansion Method ◽  
Ion Acoustic Waves ◽  
B Spline ◽  
Kudryashov Method ◽  
Ion Acoustic ◽  
Dimensional Equation ◽  
The Relationship

The trigonometric quintic B-spline scheme is used in this research paper to research Zakharov’s (ZK) nonlinear dimensional equation’s numerical solution. The ZK model’s solutions explain the relationship between the high-frequency Langmuir and the low-frequency ion-acoustic waves with many applications in optical fiber, coastal engineering, and fluid mechanics of electromagnetic waves, plasma physics, and signal processing. Three recent computational schemes (the expanded [Formula: see text]-expansion method, generalized Kudryashov method, and modified Khater method) have recently been used to investigate this model’s moving wave solution. Many innovative solutions have been established in this paper to determine the original and boundary conditions that allow numerous numerical schemes to be implemented. Here, the trigonometric quintic B-spline method is used to analyze the precision of the collected analytical solutions. To illustrate the precision of the numerical and computational solutions, distinct drawings are depicted.

Stability of ion-acoustic solitons in a multispecies plasma consisting of non-isothermal electrons

1998 ◽  
Vol 60 (1) ◽  
pp. 151-158 ◽  
Author(s):  
DEBALINA CHAKRABORTY ◽  
K. P. DAS
Keyword(s):  
Acoustic Waves ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Petviashvili Equation ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
The Stability ◽  
Perturbation Expansion Method

A modified Kadomtsev–Petviashvili equation is derived for ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons. This equation is used to investigate the stability of modified KdV solitons against long-wavelength plane-wave perturbation using the small-k perturbation expansion method of Rowlands and Infeld. It is found that modified KdV solitons are stable.

Nonlinear propagation of ion-acoustic waves and low-frequency electrostatic modes in a dusty plasma

1993 ◽  
Vol 50 (1) ◽  
pp. 37-44 ◽  
Author(s):  
U. A. Mofiz ◽  
Madhabi Islam ◽  
Zarin Ahmed
Keyword(s):  
Dusty Plasma ◽  
Acoustic Waves ◽  
Wave Scattering ◽  
Evolution Equations ◽  
Low Frequency ◽  
Nonlinear Propagation ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons

Nonlinear propagation of ion-acoustic waves and low-frequency electrostatic modes in a dusty plasma is investigated. The evolution equations of these modes are developed and solved analytically. It is found that for small grain charge usual ion-acoustic solitons may exist in a dusty plasma, but increasing grain charge destroys them and finally they may disappear. The low-frequency electrostatic mode may be localized, forming solitons, which may act as centres of wave scattering in a dusty plasma.

scholarly journals Generation of Low-Frequency Kinetic Waves at the Footpoints of Pre-Flare Coronal Loops

Solar Physics ◽  
2020 ◽  
Vol 295 (12) ◽  
Author(s):  
Alexandr Kryshtal ◽  
Anna Voitsekhovska ◽  
Oleg Cheremnykh ◽  
Istvan Ballai ◽  
Gary Verth ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Low Frequency ◽  
Small Scale ◽  
Plasma Parameters ◽  
Ion Acoustic Waves ◽  
Frequency Wave ◽  
Electric And Magnetic Fields ◽  
Ion Acoustic ◽  
Flare Process ◽  
Semi Empirical

AbstractIn this study we discuss the excitation of low-frequency plasma waves in the lower-middle chromosphere region of loop footpoints for the case when the plasma can be considered to be in a pre-flare state. It is shown that among the well-known semi-empirical models of the solar atmosphere, only the VAL (F) model together with a particular set of basic plasma parameters and amplitudes of the electric and magnetic fields supports generation of low-frequency wave instability. Our results show that it is possible to predict the onset of the flare process in the active region by using the interaction of kinetic Alfvén and kinetic ion-acoustic waves, which are solutions of the derived dispersion equation. The VAL (F) model allows situations when the main source of the aforementioned instability can be a sub-Dreicer electric field and drift plasma movements due to presence of spatial inhomogeneities. We also show that the generation of kinetic Alfvén and kinetic ion-acoustic waves can occur both, in plasma with a purely Coulomb conductivity and in the presence of small-scale Bernstein turbulence. The excitation of the small amplitude kinetic waves due to the development of low threshold instability in plasma with relatively low values of the magnetic field strength is also discussed.

Propagation of dispersive wave solutions for (3 + 1)-dimensional nonlinear modified Zakharov–Kuznetsov equation in plasma physics

2020 ◽  
Vol 34 (25) ◽  
pp. 2050227
Author(s):  
Karmina K. Ali ◽  
Aly R. Seadawy ◽  
Asif Yokus ◽  
Resat Yilmazer ◽  
Hasan Bulut
Keyword(s):  
Magnetic Field ◽  
Acoustic Waves ◽  
Uniform Magnetic Field ◽  
Expansion Method ◽  
Dispersive Wave ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions ◽  
Proposed Model ◽  
Ion Acoustic

In the current study, we instigate the four-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation. The NLmZK equation guides the attitude of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Two different methods are used, namely the sine-Gordon expansion method (SGEM) and the [Formula: see text]-expansion method to the proposed model. We have successfully constructed some topological, non-topological, and wave solutions. In addition, the 2D, 3D, and contour graphs of the solutions are also plotted under the choice of appropriate values of the parameters.

Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized G′/G$\left({\boldsymbol{G}}^{\prime }/\boldsymbol{G}\right)$-expansion method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Onur Alp Ilhan ◽  
Haci Mehmet Baskonus ◽  
M. Nurul Islam ◽  
M. Ali Akbar ◽  
Danyal Soybaş
Keyword(s):  
Acoustic Waves ◽  
Electromagnetic Waves ◽  
Evolution Equations ◽  
Nonlinear Differential Equations ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Ion Acoustic Waves ◽  
Biological Population ◽  
Complex Transformation ◽  
Internal Structures

Abstract The time-fractional generalized biological population model and the (2, 2, 2) Zakharov–Kuznetsov (ZK) equation are significant modeling equations to analyse biological population, ion-acoustic waves in plasma, electromagnetic waves, viscoelasticity waves, material science, probability and statistics, signal processing, etc. The new generalized G ′ / G $\left({G}^{\prime }/G\right)$ -expansion method is consistent, computer algebra friendly, worthwhile through yielding closed-form general soliton solutions in terms of trigonometric, rational and hyperbolic functions associated to subjective parameters. For the definite values of the parameters, some well-established and advanced solutions are accessible from the general solution. The solutions have been analysed by means of diagrams to understand the intricate internal structures. It can be asserted that the method can be used to compute solitary wave solutions to other fractional nonlinear differential equations by means of fractional complex transformation.

Large amplitude ion-acoustic waves observed in the solar wind by the Solar Orbiter

2021 ◽  
Author(s):  
David Pisa ◽  
Jan Soucek ◽  
Ondrej Santolik ◽  
Milan Maksimovic ◽  
Timothy Horbury ◽  
...  
Keyword(s):  
Solar Wind ◽  
Detailed Analysis ◽  
Acoustic Waves ◽  
Large Scale ◽  
Low Frequency ◽  
Linear Wave ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
The Time Domain ◽  
Low Frequency Waves

<p>Electric field observations of the Time Domain Sampler (TDS) receiver, a part of the Radio and Plasma Waves (RPW) instrument onboard Solar Orbiter, often exhibit very intense broadband emissions at frequencies below 10 kHz in the spacecraft frame. The RPW instrument has been operating almost continuously during the commissioning phase of the mission from March to May, the first perihelion in June, and through the first flyby of Venus in late December 2020. Nearly a year of observations allow us to perform a statistical study of ion-acoustic waves in the solar wind covering an interval of heliocentric distances between 0.5 AU to 1 AU. The occurrence of low-frequency waves peaks around perihelion in June at distances of 0.5 AU and decreases with increasing distances, with only a few waves detected per day in late September at ~1 AU. A more detailed analysis of triggered waveform snapshots shows the typical wave frequency at about 3 kHz and wave power about 5e-2 mV<sup>2</sup>/m<sup>2</sup>. The distribution of the relative phase between two components of the projected E-field in the Spacecraft Reference Frame (SRF) shows a mostly linear wave polarization. These waves are interpreted as strongly Doppler-shifted ion-acoustic waves, generated by solar wind ion beams and often accompany large-scale solar wind structures. A detailed analysis of the Doppler-shift using solar wind data from a Proton and Alpha particle Sensor (PAS), a part of Solar Wind Analyzer (SWA), is done for several examples.</p>

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