scholarly journals Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma

2016 ◽  
Vol 6 ◽  
pp. 590-593 ◽  
Author(s):  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Solitary Wave ◽  
Dusty Plasma ◽  
Dynamical Equation ◽  
Three Dimensional ◽  
Solitary Wave Solutions ◽  
Ion Temperature ◽  
Wave Solutions ◽  
Ion Acoustic

Construction of the numerical and analytical wave solutions of the Joseph–Egri dynamical equation for the long waves in nonlinear dispersive systems

2020 ◽  
Vol 34 (30) ◽  
pp. 2050289
Author(s):  
Abdulghani R. Alharbi ◽  
M. B. Almatrafi ◽  
Aly R. Seadawy
Keyword(s):  
Solitary Wave ◽  
Numerical Solution ◽  
Evolution Equations ◽  
Dynamical Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability

The Kudryashov technique is employed to extract several classes of solitary wave solutions for the Joseph–Egri equation. The stability of the achieved solutions is tested. The numerical solution of this equation is also investigated. We also present the accuracy and the stability of the numerical schemes. Some two- and three-dimensional figures are shown to present the solutions on some specific domains. The used methods are found useful to be applied on other nonlinear evolution equations.

Dispersive solitary wave solutions of nonlinear further modified Korteweg–de Vries dynamical equation in an unmagnetized dusty plasma

2018 ◽  
Vol 33 (37) ◽  
pp. 1850217 ◽  
Author(s):  
Mujahid Iqbal ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Solitary Wave ◽  
Dusty Plasma ◽  
Electrostatic Potential ◽  
Dynamical Equation ◽  
Graphical Representation ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
De Vries

In this work, we consider the propagation of one-dimensional nonlinear unmagnetized dusty plasma, by using the reductive perturbation technique to formulate the nonlinear mathematical model which is further modified Korteweg–de Vries (fmKdV) dynamical equation. We use the extend form of two methods, auxiliary equation mapping and direct algebraic methods, to investigate the families of dust and ion solitary wave solutions of one-dimensional nonlinear fmKdV. These new exact and solitary wave solutions, which represent the electrostatic potential and pressure for fmKdV, and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica.

Diverse bistable dark novel explicit wave solutions of cubic–quintic nonlinear Helmholtz model

2021 ◽  
pp. 2150441
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
General Model ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Solitary Wave Solutions ◽  
Computational Schemes ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

This paper examines three different recent computational schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel solitary wave solutions of cubic–quintic nonlinear Helmholtz (CQ–NLH) model. This model is considered as a general model of the well-known Schrödinger equation where it takes into account the effects of backward scattering that are neglected in the more common nonlinear Schrödinger model. Many distinct wave solutions are explained in the different formulas, such as trigonometric, rational, and hyperbolic formulas. These solutions are described in some precise sketches in two- and three-dimensional. The methods’ performance is explained to demonstrate their effectiveness and power.

Stability of ion acoustic solitary waves in a magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution

2013 ◽  
Vol 80 (1) ◽  
pp. 89-112
Author(s):  
Jayasree Das ◽  
Anup Bandyopadhyay ◽  
K. P. Das
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Solitary Wave ◽  
Velocity Distribution ◽  
Plasma Phys ◽  
Solitary Wave Solutions ◽  
Long Wavelength ◽  
Zk Equation ◽  
Wave Solutions ◽  
Ion Acoustic

AbstractSchamel's modified Korteweg-de Vries–Zakharov–Kuznetsov (S-ZK) equation, governing the behavior of long wavelength, weak nonlinear ion acoustic waves propagating obliquely to an external uniform static magnetic field in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, admits solitary wave solutions having a sech4 profile. The higher order stability of this solitary wave solution of the S-ZK equation has been analyzed with the help of multiple-scale perturbation expansion method of Allen and Rowlands (Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413; 1995 J. Plasma Phys. 53, 63). The growth rate of instability is obtained correct to the order k2, where k is the wave number of a long wavelength plane wave perturbation. It is found that the lowest order (at the order k) instability condition is strongly sensitive to the angle of propagation (δ) of the solitary wave with the external uniform static magnetic field, whereas at the next order (at the order k2) the solitary wave solutions of the S-ZK equation are unstable irrespective of δ. It is also found that the growth rate of instability up to the order k2 for the electrons having Boltzmann distribution is higher than that of the non-thermal electrons having vortex-like distribution for any fixed δ.

Stability analysis and applications of traveling wave solutions of three-dimensional nonlinear modified Zakharov–Kuznetsov equation in a magnetized plasma

2018 ◽  
Vol 33 (25) ◽  
pp. 1850145 ◽  
Author(s):  
Abdullah ◽  
Aly R. Seadawy ◽  
Jun Wang
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Electrostatic Field ◽  
Three Dimensional ◽  
Field Potential ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Magnetized Plasma ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Propagation of three-dimensional nonlinear solitary waves in a magnetized electron–positron plasma is analyzed. Modified extended mapping method is further modified and applied to three-dimensional nonlinear modified Zakharov–Kuznetsov equation to find traveling solitary wave solutions. As a result, electrostatic field potential, electric field, magnetic field and quantum statistical pressure are obtained with the aid of Mathematica. The new exact solitary wave solutions are obtained in different forms such as periodic, kink and anti-kink, dark soliton, bright soliton, bright and dark solitary waves, etc. The results are expressed in the forms of trigonometric, hyperbolic, rational and exponential functions. The electrostatic field potential and electric and magnetic fields are shown graphically. The soliton stability of these solitary wave solutions is analyzed. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.

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