Ion Acoustic Solitary Wave Solutions Research Articles

Ion Acoustic Solitary Wave Solutions to mKdV-ZK Model in Homogeneous Magnetized Plasma

In this exploration, we reflect on the wave transmission of three-dimensional (3D) nonlinear electron–positron magnetized plasma, counting both hot as well as cold ion. Treated equation acquiesces to nonlinear-modified KdV-Zakharov–Kuznetsov (mKdV-ZK) dynamical 3D form. The model is integrated by the φ 6 -model expansion scheme and invented few families of ion acoustic solitonic propagation results in term of Jacobi elliptic functions. Various shock waves, bullet like bright soliton, dark soliton, singular soliton, as well as periodic signal solutions, are formed from the Jacobi elliptic solution for different parametric constraints. Some of the solutions are illustrated graphically and analyzed width and height due to change of exist parameters in the solutions. Figures are provided to explain the wave natures and effects of nonlinear and fractional parameters are presented in the same two-dimensional (2D) plots.

Small amplitude ion-acoustic solitary waves in a four-component magneto- rotating plasma with a modified Cairns-Tsallis distribution

The small amplitude ion-acoustic solitary waves in the magneto-rotating plasma consisting of cold fluid ions, hot positrons, and the two-temperature electrons (cold and hot electrons) are investigated when the electrons obey a modified Cairns-Tsallis distribution. By using the reductive perturbation method, we derive the Korteweg–de Vries equation and the modified Korteweg–de Vries equation and obtain the small amplitude ion-acoustic solitary wave solutions. The dependences of solitary wave solutions on the nonextensive q-parameter, the nonthermal α-parameter and the plasma physical quantities are analyzed numerically. We show the significant effects of the nonextensive q-parameter and the nonthermal α-parameter etc on the ion-acoustic solitary waves.

Structure of analytical ion-acoustic solitary wave solutions for the dynamical system of nonlinear wave propagation

Abstract In the present study, the ion-acoustic solitary wave solutions for Kadomtsev–Petviashvili (KP) equation, potential KP equation, and Gardner KP equation are constructed. The nonlinear KP equations are studying the nonlinear process of waves without collisions plasma and having non-isothermal electrons and cold ions. Two-dimensional ion-acoustic solitary waves (IASWs) in magnetized plasma are consisting of electrons and ions. We obtained the ion-acoustic solitary wave solutions same as dark and bright, kink and anti-kink wave solitons. The physical phenomena of various structures for IASWs are represented graphically with symbolic computations. These results are more helpful in the development of soliton dynamics, quantum plasma, dynamic of adiabatic parameters, fluid dynamics, and industrial phenomena.

Dynamical study of nonlinear ion acoustic waves in presence of charged space debris at Low Earth Orbital (LEO) plasma region

We consider the nonlinear ion acoustic wave induced by orbiting charged space debris objects in the plasma environment generated at the Low Earth Orbital (LEO) region. The generated nonlinear ion acoustic wave is shown to be governed by a forced Korteweg-de Vries (fKdV) equation with the forcing function dependent on the charged space debris function. For a specific relationship between the forcing debris function and the nonlinear ion acoustic wave, the forced KdV equation turns out to be a completely integrable system; where the debris function obeys a definite nonholonomic constraint. A special exact accelerated soliton solution (velocity of the soliton changes over time whereas its amplitude remains constant) has been derived for the ion acoustic wave for the first time. On the other hand, the amplitude of the solitonic debris function varies with time, and its shape changes during the propagation. Approximate ion acoustic solitary wave solutions with time varying amplitudes and velocities have been derived for different types of weakly localized charged debris functions. Possible applications of the obtained results in space plasma physics are stated along with future directions for research.

Bifurcation Analysis for Small-Amplitude Nonlinear and Supernonlinear Ion-Acoustic Waves in a Superthermal Plasma

Abstract Bifurcation analysis of small-amplitude nonlinear and supernonlinear periodic ion-acoustic waves (SNPIAWs) is reported in a three-constituent superthermal plasma composing of cold fluid ions and kappa-distributed electrons of two temperatures (cold and hot). Using the reductive perturbation technique, the plasma system is studied under the Korteweg-de Vries (KdV) and the modified KdV (mKdV) equations. Furthermore, the KdV and mKdV equations are transformed into planar dynamical systems applying travelling wave transfiguration. Possible qualitative phase profiles for the corresponding dynamical systems controlled by system parameters ( κ , α c , α h $\kappa,{\alpha_{c}},{\alpha_{h}}$ and f) are shown. Small-amplitude SNPIAW solution for the mKdV equation is presented for the first time. Small-amplitude nonlinear periodic ion-acoustic wave (NPIAW) and ion-acoustic solitary wave solutions (IASWS) for both the KdV and mKdV equations are obtained. Effects of parameters κ and α h on IASW, NPIAW and SNPIAW solutions are investigated.

Ion-acoustic solitary wave solutions of nonlinear damped Korteweg–de Vries and damped modified Korteweg–de Vries dynamical equations

By using the reductive perturbation technique, the nonlinear dust ion-acoustic solitary wave models of the damped Korteweg–de Vries (D-KdV) and modified damped Korteweg–de Vries (D-mKdV) equations are formulated. We constructed the more general and new solitary wave solutions of nonlinear damped KdV and damped mKdV equations by using the modified mathematical technique. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of adiabatic parameters, dynamics of fluid and problems of biomedical, industrial phenomena. The new solutions are obtained in the shape of dark solitons, bright solitons, traveling wave and kink and anti-kink wave solitons. We show the physical structure of new solutions by two and three-dimensions graphical to know the physical interpretation of different structure of dust ion-acoustic solitary wave. The calculations show that this new technique is more powerful, effective, straightforward, and fruitfulness to study analytically other nonlinear complex physical models in plasma physics, mathematical physics, fluid mechanics, hydrodynamics, mathematical biology and many other physical sciences.

Construction of bright–dark solitons and ion-acoustic solitary wave solutions of dynamical system of nonlinear wave propagation

The nonlinear (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) equations deal with the nonlinear behavior of waves in collision-less plasma, which contains non-isothermal cold ions and electrons. Two-dimensional dust acoustic solitary waves (DASWs) in magnetized plasma, which consist of trapped electrons and ions are leading to (2 + 1)-dim (ZK) equation by using the perturbation technique. We found the solitary wave solutions of (2 + 1)-dimensional (ZK)-equation, generalized (ZK)-equation and generalized form of modified (ZK)-equation by implementing the modified mathematical method. As a result, we obtained the bright–dark solitons, traveling wave and solitary wave solutions. The physical structure of obtained solutions is represented in 2D and 3D, graphically with the help of Mathematica.

Analytical solitary wave solution of the dust ion acoustic waves for the damped forced modified Korteweg-de Vries equation in q-nonextensive plasmas

Analytical solitary wave solution of the dust ion acoustic waves is studied due to the damped forced modified Korteweg-de Vries equation in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, q-nonextensive electrons, and neutral particles in the presence of external periodic force. Using reductive perturbation technique, the damped forced modified Korteweg-de Vries equation is obtained for the dust ion acoustic waves. Momentum consevation law is used to obtain the dust ion acoustic solitary wave solutions in the framework of the damped forced modified Korteweg-de Vries equation. The effects of different physical parameters such as entropic index, dust ion collisional frequency, strength and frequency of the external periodic force, speed of the traveling wave and the parameter which is the ratio between the unperturbed densities of the dust ions and electrons are investigated on the analytical solution of the dust ion acoustic waves. It is observed that those parameters have significant effects on the structures of the damped forced dust ion acoustic solitary waves. The results of the present paper may have applications in laboratory and space plasma environments.

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

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.

Modified KdV–Zakharov–Kuznetsov dynamical equation in a homogeneous magnetised electron–positron–ion plasma and its dispersive solitary wave solutions

Propagation of three-dimensional nonlinear ion-acoustic solitary waves and shocks in a homogeneous magnetised electron–positron–ion plasma is analysed. Modified extended mapping method is introduced to find ion-acoustic solitary wave solutions of the three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation. As a result, solitary wave solutions (which represent electrostatic field potential), electric fields, magnetic fields and quantum statistical pressures are obtained with the aid of Mathematica. These new exact solitary wave solutions are obtained in different forms such as periodic, kink and antikink, dark soliton, bright soliton, bright and dark solitary wave etc. The results are expressed in the forms of hyperbolic, trigonometric, exponential and rational functions. The electrostatic field potential and electric and magnetic fields are shown graphically. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical and physical problems.

Solitary wave solution and dynamic transition of dust ion acoustic waves in a collisional nonextensive dusty plasma with ionization effect

The solitary wave solution and dynamic transition of dust ion acoustic waves (DIAWs) are studied in an unmagnetized collisional dusty plasma, which consists of negatively charged dust fluid, positively charged ions, q-nonextensive electrons, and background neutral particles, considering the ionization effect, ion loss, ion–neutral, ion–dust, and dust–neutral collisions. Using reductive perturbation technique (RPT) the damped Korteweg–de Vries (DKdV) equation and the damped modified Korteweg–de Vries (DMKdV) equation are derived. Using momentum conservation law, dust ion acoustic solitary wave solutions (DIASWSs) are obtained for the DKdV and MDKdV equations. Effects of nonextensive parameter (q) and ion–dust collisional frequency (νid) are presented on the DIASWSs. Effects of ion–dust collisional frequency (νid), ion–neutral collisional frequency (νin) and ion loss rate (νl) on DIAWs are investigated considering an external periodic perturbation through three-dimensional phase portrait and time-series analysis. It is found that νid, νin and νl significantly affect on the dynamics of the perturbed DIAWs and play a pivotal role in the transition from quasiperiodic and chaotic motions to periodic motion.

Ion acoustic solitary wave solutions of two‐dimensional nonlinear Kadomtsev–Petviashvili–Burgers equation in quantum plasma

Propagation of two‐dimensional nonlinear ion‐acoustic solitary waves and shocks in a dissipative quantum plasma is analyzed. By applying the reductive perturbation theory, the two‐dimensional ion acoustic solitary waves in a dissipative quantum plasma lead to a nonlinear Kadomtsev–Petviashvili–Burgers (KPB) equation. By implementing extended direct algebraic mapping, extended sech‐tanh, and extended direct algebraic sech methods, the ion solitary traveling wave solutions of the two‐dimensional nonlinear KPB equation are investigated. An analytical as well as numerical solution of the two‐dimensional nonlinear KPB equation is obtained and analyzed with the effects of external electric field and ion pressure. Copyright © 2016 John Wiley & Sons, Ltd.

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

We consider the propagation of three-dimensional nonlinear magnetized two-ion-temperature dusty plasma. The problem formulation of this mathematical model leads to nonlinear extended Zakharov–Kuznetsov (EZK) dynamical equation in three-dimensional by applying the reductive perturbation theory. We found the families of dust and ion solitary wave solutions of the three-dimensional nonlinear EZK dynamical equation using the auxiliary equation mapping method and direct algebraic mapping method.

Effect of nonthermal electrons and positrons on ion-acoustic solitary waves in a plasma with warm drifting ions

Using Sagdeev potential technique, ion-acoustic solitary waves have been theoretically studied in collisionless unmagnetized plasma consisting of nonthermal electrons, nonthermal positrons and warm drifting positive ions. Ion-acoustic solitary wave solutions have been obtained and its profiles have been numerically analyzed with respect to plasma parameters. The nonthermal parameters and temperatures are shown to play significant role on the formation and nature of solitary waves. It is shown that the nature, amplitude and width of lower- and higher-order solitons depend sensitively on these plasma parameters. The dependence of Sagdeev potential profile on different plasma parameters has also been examined. We have found that stronger nonthermality leads to shorter and wider solitons.

Ion-Acoustic Solitary Waves near Double Layers

The possibility of ion-acoustic solitary-wave solutions in the uniform plasma on the high-potential side of double layer is investigated. Based on a fluid model of the double layer, it is found that both compressive and rarefactive solitary waves are allowed. Curves are presented which show the regions in parameter space in which these solutions exist.