W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations

2021 ◽  
pp. 2150468
Author(s):  
Youssoufa Saliou ◽  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
M. S. Osman ◽  
Doka Serge Yamigno ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Singular Function ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Quantum Electron ◽  
Ion Acoustic ◽  
Trigonometric Function Solutions

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

A model equation for non-resonant interacting ion acoustic plasma waves

1998 ◽  
Vol 60 (2) ◽  
pp. 275-288 ◽  
Author(s):  
ATTILIO MACCARI
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Plasma Waves ◽  
Nonlinear Evolution Equations ◽  
Localized Solutions ◽  
Asymptotic Perturbation Method ◽  
Ion Acoustic ◽  
Spatio Temporal ◽  
Asymptotic Perturbation ◽  
Group Velocities

The interaction among non-resonant ion acoustic plasma waves with different group velocities that are not close to each other is studied by an asymptotic perturbation method, based on Fourier expansion and spatio-temporal rescaling. It is shown that the nonlinear Schrödinger equation is not adequate, and instead a model system of nonlinear evolution equations is necessary to describe oscillation amplitudes of Fourier modes. This system is C-integrable, i.e. it can be linearized through an appropriate transformation of the dependent and independent variables. We demonstrate that the subclass of localized solutions gives rise to a solitonic phenomenology. These solutions propagate with the relative group velocity and maintain their shape during a collision, the only change being a phase shift. Numerical calculations confirm the validity of these predictions.

scholarly journals The Improvedexp⁡-Φξ-Expansion Method and New Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Guiying Chen ◽  
Xiangpeng Xin ◽  
Hanze Liu
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
New Exact Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

Theexp(-Φ(ξ))-expansion method is improved by presenting a new auxiliary ordinary differential equation forΦ(ξ). By using this method, new exact traveling wave solutions of two important nonlinear evolution equations, i.e., the ill-posed Boussinesq equation and the unstable nonlinear Schrödinger equation, are constructed. The obtained solutions contain Jacobi elliptic function solutions which can be degenerated to the hyperbolic function solutions and the trigonometric function solutions. The present method is very concise and effective and can be applied to other types of nonlinear evolution equations.

Effect of finite ion-temperature on ion-acoustic solitary waves in an inhomogeneous plasma

1981 ◽  
Vol 59 (6) ◽  
pp. 719-721 ◽  
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Acoustic Waves ◽  
Inhomogeneous Plasma ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
Velocity Of Propagation

The propagation of weakly nonlinear ion–acoustic waves in an inhomogeneous plasma is studied taking into account the effect of finite ion temperature. It is found that, whereas both the amplitude and the velocity of propagation decrease as the ion–acoustic solitary wave propagates into regions of higher density, the effect of a finite ion temperature is to reduce the amplitude but enhance the velocity of propagation of the solitary wave.

Second harmonic interference patterns of ion-acoustic waves

1982 ◽  
Vol 27 (3) ◽  
pp. 543-552
Author(s):  
L. Schott
Keyword(s):  
Acoustic Waves ◽  
Second Harmonic ◽  
Physical Optics ◽  
Third Wave ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Linear Pattern ◽  
The Third ◽  
Ion Acoustic ◽  
Local Wave

The interaction of two weakly nonlinear sinusoidal ion-acoustic waves produces mainly a fundamental and a second harmonic diffraction pattern. The former is similar to the double slit pattern well known from physical optics, while it is found that the latter resembles a linear pattern generated by the superposition of three waves. The third wave is formed by mutual nonlinear interaction of the two fundamental waves. The intensity of the second harmonic pattern is modulated by the recurrence effect and it depends also on the angle between the local wave vectors.

Weakly nonlinear dust ion-acoustic waves in a charge varying dusty plasma with non-thermal electrons

2008 ◽  
Vol 74 (2) ◽  
pp. 245-259 ◽  
Author(s):  
MOULOUD TRIBECHE ◽  
ABDERREZAK BERBRI
Keyword(s):  
Dusty Plasma ◽  
Acoustic Waves ◽  
Oscillatory Behavior ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Ion Acoustic ◽  
De Vries ◽  
Dust Ion Acoustic Waves ◽  
A Charge

AbstractThe weakly nonlinear dynamics of dust ion-acoustic waves (DIAWs) are investigated in a dusty plasma consisting of hot ion fluid, variable charge stationary dust grains and non-thermally distributed electrons. The Korteweg–de Vries equation, as well as the Korteweg–de Vries–Burgers equation, are derived on the basis of the well-known reductive perturbation theory. It is shown that, due to electron non-thermality and finite ion temperature, the present dusty plasma model can support compressive as well as rarefactive DIA solitary waves. Furthermore, there may exist collisionless DIA shock-like waves which have either monotonic or oscillatory behavior, the properties of which depend sensitively on the number of fast non-thermal electrons. The results complement and provide new insights into previously published results on this problem (Mamun, A. A. and Shukla, P. K. 2002 IEEE Trans. Plasma Sci. 30, 720).

The influence of ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves

1992 ◽  
Vol 48 (3) ◽  
pp. 477-486
Author(s):  
E. J. Parkes
Keyword(s):  
Acoustic Waves ◽  
Averaging Method ◽  
Modulational Instability ◽  
Relativistic Effects ◽  
Instability Criterion ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Nonlinear Dispersion Relation ◽  
Ion Acoustic ◽  
Unmagnetized Plasma

The influence of ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves in a collisionless unmagnetized plasma is investigated. An averaging method is used to derive a weakly nonlinear dispersion relation, from which the instability criterion is deduced. Conflicting results in the literature are resolved.

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