scholarly journals Nonlinear dynamical properties of solitary wave solutions for Zakharov-Kuznetsov equation in a multicomponent plasma

2021 ◽  
Vol 67 (6 Nov-Dec) ◽  
Author(s):  
U.M. Abdelsalam
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Traveling Wave Solutions ◽  
Reductive Perturbation Method ◽  
Physical Parameters ◽  
Nonlinear Dynamical ◽  
Multicomponent Plasma ◽  
Wave Solutions ◽  
Laboratory Plasmas ◽  
Component Plasma

Using the reductive perturbation method, we have derived the Zakharov-Kuznetsov (ZK) equation for a multi-component plasma model consisting of electrons, positrons and the uid ions with positive and negative charges. The extended homogenous balance method has been applied to obtain the soliton solution in addition to many traveling wave solutions. various physical parameters have different effects on the profile of the solitary wave pulses which can show the propagation of the ion acoustic waves in laboratory plasmas and many astrophysical plasma systems as in Earth's ionosphere.

scholarly journals Modulational Instability of Ion-Acoustic Waves and Associated Envelope Solitons in a Multi-Component Plasma

Gases ◽  
2021 ◽  
Vol 1 (3) ◽  
pp. 148-155
Author(s):  
Subrata Banik ◽  
Nadiya Mehzabeen Heera ◽  
Tasfia Yeashna ◽  
Md. Rakib Hassan ◽  
Rubaiya Khondoker Shikha ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Modulational Instability ◽  
Reductive Perturbation Method ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Stable Domain ◽  
Laboratory Plasmas ◽  
Electrons And Positrons ◽  
Ion Acoustic ◽  
Component Plasma

A generalized plasma model with inertial warm ions, inertialess iso-thermal electrons, super-thermal electrons and positrons is considered to theoretically investigate the modulational instability (MI) of ion-acoustic waves (IAWs). A standard nonlinear Schrödinger equation is derived by applying the reductive perturbation method. It is observed that the stable domain of the IAWs decreases with ion temperature but increases with electron temperature. It is also found that the stable domain increases by increasing (decreasing) the electron (ion) number density. The present results will be useful in understanding the conditions for MI of IAWs which are relevant to both space and laboratory plasmas.

scholarly journals Ion-Acoustic Solitary Wave Solutions of Three-Dimensional Zakharov-KuznetsovBurgers Equation for Dust Ion Acoustic Waves and Their Applications

2019 ◽  
Vol 2 (1) ◽  
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Field Potential ◽  
Traveling Wave Solutions ◽  
Physical Models ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ion Acoustic

Modified extended mapping method is further modified to discover traveling wave solutions of non- linear complex physical models, arising in various fields of applied sciences. The method is applied to three-dimensional ZakharovKuznetsov-Burgers equation in magnetized dusty plasma. Consequently different kinds of families of exact traveling wave solutions that represent electric field potential, electric and magnetic fields are fruitfully surveyed, with the help of Mathematica. The obtained novel exact traveling wave solutions are in different forms such as bright and dark solitary wave, periodic solitary wave, dark and bright soliton, etc., that are represented in the forms of trigonometric, hyperbolic, exponential and rational functions. The properties of some of the novel traveling wave solutions are shown by figures. The obtained results exhibit the effectiveness, power and exactness of the method that can be used for many other nonlinear problems.

scholarly journals Cylindrical and Spherical Solitons at the Critical Density of Negative Ions in a Generalised Multicomponent Plasma

1991 ◽  
Vol 44 (5) ◽  
pp. 523 ◽  
Author(s):  
GC Das ◽  
Kh Ibohanbi Singh
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Critical Density ◽  
Negative Ions ◽  
Ion Acoustic Waves ◽  
Multicomponent Plasma ◽  
Laboratory Plasmas ◽  
Ion Acoustic ◽  
Geometrical Effects

Propagation of nonlinear ion-acoustic waves in generalised multicomponent plasmas bounded by cylindrical and spherical geometries is investigated. At the critical density of negative ions where the nonlinearity of the Korteweg-deVries (K-dV) equation vanishes, the ion-acoustic solitary wave is described by a modified K-dV (mK-dV) equation. It is also emphasised that near the critical density neither the K-dV nor mK-dV equation is sufficient to describe fully the ion-acoustic waves and thus there is a need to derive a further mK-dV (fmK-dV) equation in the vicinity of this critical density. Furthermore, the amplitude variations of the K-dV and mK-dV solitons depending on the limitations of geometrical effects are also discussed, emphasising that the results could be of interest for diagnosing the soliton properties of laboratory plasmas.

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

Traveling Wave Solutions of a Two-Component Dullin–Gottwald–Holm System

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Jiyu Zhong ◽  
Shengfu Deng
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Planar Systems

In this paper, we investigate the traveling wave solutions of a two-component Dullin–Gottwald–Holm (DGH) system. By qualitative analysis methods of planar systems, we investigate completely the topological behavior of the solutions of the traveling wave system, which is derived from the two-component Dullin–Gottwald–Holm system, and show the corresponding phase portraits. We prove the topological types of degenerate equilibria by the technique of desingularization. According to the dynamical behaviors of the solutions, we give all the bounded exact traveling wave solutions of the system, including solitary wave solutions, periodic wave solutions, cusp solitary wave solutions, periodic cusp wave solutions, compactonlike wave solutions, and kinklike and antikinklike wave solutions. Furthermore, to verify the correctness of our results, we simulate these bounded wave solutions using the software maple version 18.

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

scholarly journals The Modified Simple Equation Method for Exact and Solitary Wave Solutions of Nonlinear Evolution Equation: The GZK-BBM Equation and Right-Handed Noncommutative Burgers Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Kamruzzaman Khan ◽  
M. Ali Akbar ◽  
Norhashidah Hj. Mohd. Ali
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Simple Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Modified Simple Equation Method ◽  
Bbm Equation

The modified simple equation method is significant for finding the exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this paper, we bring in the modified simple equation (MSE) method for solving NLEEs via the Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony (GZK-BBM) equation and the right-handed noncommutative Burgers' (nc-Burgers) equations and achieve the exact solutions involving parameters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. It is established that the MSE method offers a further influential mathematical tool for constructing the exact solutions of NLEEs in mathematical physics.

BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED TWO-COMPONENT CAMASSA–HOLM EQUATION

2012 ◽  
Vol 22 (12) ◽  
pp. 1250305 ◽  
Author(s):  
JIBIN LI ◽  
ZHIJUN QIAO
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Breaking Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Kink Wave

In this paper, we apply the method of dynamical systems to a generalized two-component Camassa–Holm system. Through analysis, we obtain solitary wave solutions, kink and anti-kink wave solutions, cusp wave solutions, breaking wave solutions, and smooth and nonsmooth periodic wave solutions. To guarantee the existence of these solutions, we give constraint conditions among the parameters associated with the generalized Camassa–Holm system. Choosing some special parameters, we obtain exact parametric representations of the traveling wave solutions.

scholarly journals Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Qing Meng ◽  
Bin He
Keyword(s):  
Solitary Wave ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Sufficient Conditions ◽  
Traveling Wave Solutions ◽  
Type Equation ◽  
Periodic Wave ◽  
Point Of View ◽  
Bifurcation Method ◽  
Wave Solutions

The generalized HD type equation is studied by using the bifurcation method of dynamical systems. From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, all possible exact parametric representations of the bounded waves are presented and their relations are stated.

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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