: It is shown that under certain approximations the basic system of equations governing the propagation of ion acoustic waves can be reduced to the Kortweg-deVries equation. (Author)

On the propagation of ion acoustic solitary waves of small amplitude.

Dynamics of the positron acoustic waves in electron–positron–ion (e–p–i) magnetoplasmas with $$\kappa $$
 -distributed hot electrons and positrons is investigated in the frameworks of the Kadomtsev–Petviashili (KP) and modified Kadomtsev–Petviashili (mKP) equations. Employing the reductive perturbation technique, the KP and mKP equations are derived. Using the bifurcation theory of planar dynamical systems, the positron acoustic solitary wave solutions, the kink and anti-kink wave solutions are obtained. Considering an external periodic perturbation in the electron–positron–ion magnetoplasmas, the perturbed KP and mKP equations are studied via some qualitative and quantitative approaches. To corroborate in the fact that the perturbed KP and mKP equations can indeed give rise to the quasiperiodic and chaotic motions, the phase plane plots, time series plots, and the Poincare section are used. The quasiperiodic and developed chaos can be observed for the perturbed positron acoustic waves. The frequency (
 $$\omega $$
 ) of the external periodic perturbation plays the role of the switching parameter in chaotic motions of the perturbed positron acoustic waves through quasiperiodic route to chaos. This work can be useful to understand the dynamics of nonlinear electromagnetic perturbations in space and laboratory plasmas consisting of $$\kappa $$
 -distributed hot electrons and positrons.

Dynamics of the positron acoustic waves in electron–positron–ion magnetoplasmas

A nonlinear propagation of modified ion-acoustic (mIA) shock waves in a relativistic degenerate plasma (containing inertial viscous positive and negative ion fluids, relativistic electron fluids, and negatively charged immobile heavy ions) has been investigated theoretically The modified Burgers (mB) and further modified Burgers (FmB) equations have been derived by adopting reductive perturbation technique The solutions of both mB and FmB equations have been numerically analyzed to characterize the basic features of mIA shock waves The basic properties (speed, amplitude, width, etc) of these electrostatic shock waves are found to be significantly modified by the effects of negatively charged static heavy ions and the plasma particle number densities It is found that the properties of these shock waves obtained from this analysis are significantly different from those obtained from the analysis of standard Burgers equation The implications of our results in space and interstellar compact objects like non-rotating white dwarfs, neutron stars, etc are briefly discussed

Modeling of modified ion-acoustic shock waves in a relativistic electron degenerate multi-ion plasma for higher order nonlinearity

The generalized KadomtsevPetviashvili modified equal width-Burgers (KP-MEW-Burgers) equation is introduced for the first time. The qualitative change of the traveling wave solutions of the KP-MEW-Burgers equation is studied using numerical simulations. Considering an external periodic perturbation, the periodic and chaotic motions of the perturbed KP-MEW-Burgers equation are investigated by using the phase projection analysis, time series analysis, Poincare section and bifurcation diagram. The parameter a (nonlinear coefficient) plays a crucial role in the periodic motions and chaotic motions through period doubling route to chaos of the perturbed KP-MEW-Burgers equation.

Dynamics of the generalized KP-MEW-Burgers equation with external periodic perturbation

A theoretical investigation is made on the positron-acoustic (PA) shock waves (SHWs) in an unmagnetized electron-positron-ion plasma containing immobile positive ions, cold mobile positrons, and hot positrons and electrons following the kappa (κ) distribution. The cold positron kinematic viscosity is taken into account, and the reductive perturbation method is used to derive the Burgers equation. It is found that the viscous force acting on cold mobile positron fluid is a source of dissipation and is responsible for the formation of the PA SHWs. It is also observed that the fundamental properties of the PA SHWs are significantly modified by the effects of different parameters associated with superthermal (κ distributed) hot positrons and electrons.

Positron-acoustic shock waves associated with cold viscous positron fluid in superthermal electron-positron-ion plasmas

Dust ion-acoustic traveling waves are studied in a magnetized dusty plasma in presence of static dust and non-extensive distributed electrons in the framework of Zakharov-Kuznesstov-Burgers (ZKB) equation. System of coupled nonlinear ordinary differential equations is derived from ZKB equation, and equilibrium points are obtained. Nonlinear wave phenomena are studied numerically using fourth order Runge-Kutta method. The change from unstable to stable solution and consequently to asymptotic stable of dust ion acoustic traveling waves is studied through dynamical system approach. It is found that some dramatical features emerge when the non-extensive parameter and the dust concentration parameters are varied. Behavior of the solution of the system changes from unstable to stable and stable to asymptotic stable depending on the value of the non-extensive parameter. It is also observed that when the dust concentration is increased the solution pattern is changed from oscillatory shocks to periodic solution. Thus, non-extensive and dust concentration parameters play crucial roles in determining the nature of the stability behavior of the system. Thus, the non-extensive parameter and the dust concentration parameters can be treated as bifurcation parameters.

The roles of non-extensivity and dust concentration as bifurcation parameters in dust-ion acoustic traveling waves in magnetized dusty plasma

Ion-acoustic shock waves (IASWs) in a homogeneous unmagnetized plasma, comprising superthermal electrons, positrons, and singly charged adiabatically hot positive ions are investigated via two-dimensional nonplanar Kadomstev–Petviashvili–Burgers (KPB) equation. It is found that the profiles of the nonlinear shock structures depend on the superthermality of electrons. The influence of other plasma parameters such as, ion kinematic viscosity and ion temperature, is discussed in the presence of superthermal electrons in nonplanar geometry. It is also seen that the IASWs propagating in cylindrical/spherical geometry with transverse perturbation will be deformed as time goes on.

Nonplanar ion-acoustic shocks in electron–positron–ion plasmas: Effect of superthermal electrons

The basic features of planar and nonplanar time dependent ion-acoustic two-soliton systems have been studied in a three component unmagnetized, collisionless quantum plasma consisting of inertialess electrons and positrons. Using the reductive perturbation technique (RPT), we have derived the Korteweg–de Vries equation for our model. The effects of several parameters on the properties of ion-acoustic two-soliton systems in quantum electron–positron–ion plasmas have been discussed in planar and nonplanar geometries. It has been shown that the properties of ion-acoustic two-soliton systems are affected significantly due to cylindrical and spherical geometries. The amplitude of the cylindrical two-soliton system is smaller than that of the spherical two-soliton system for small values of |τ|. The propagation of ion-acoustic two-soliton systems is quite different from the propagation of ion-acoustic two-soliton systems in a nonplanar geometry. The present investigation may have relevance in the study of the propagation of ion-acoustic two-soliton systems in space and laboratory plasmas.

Nonplanar ion-acoustic two-soliton systems in quantum electron–positron–ion plasmas

Cylindrical Zakharov–Kuznestov equation for ion-acoustic waves comprising of ions and electrons featuring non-extensive distribution are derived from the fluid equations through reductive perturbation technique. System of first order ordinary differential equations is obtained from Zakharov–Kuznestov equation through dynamical system approach and ultimately it is solved using numerical method. It is found that the electron to positron ratio parameter and the non-extensive distributed parameter due to electron play crucial role on the solution.

https://www.tpbin.com/Uploads/Subjects/56b3f14a-d484-4ba7-b568-1ca09f46bc48.pdf

Cylindrical Zakharov–Kuznestov equation for ion-acoustic waves with electrons featuring non-extensive distribution

The nonlinear wave structures of ion acoustic waves in magnetized plasma comprising ions, non-extensive distributed electrons and kinematic viscosity are investigated through dynamical study. In a bounded cylindrical geometry Zakharov–Kuznestov–Burger (ZKB) equation is derived, for the first time, using reductive perturbation technic. System of coupled nonlinear ordinary differential equations is derived from ZKB equation and is solved numerically using fourth order Runge–kutta method. Equilibrium points are obtained and the features are studied dynamically in the neighbourhood of these points. With the variation of the non-extensive parameter and the kinematic viscosity parameter some important features in the nonlinear waves like oscillatory shocks to steady state propagation and vis-a-vis steady state propagation to oscillatory shocks emerge. When the values of the non-extensive parameter decrease, the phase portrait of the system shows that the change from stable spiral to stable closed and stable to unstable equilibrium happens . When the effect of dissipative term i.e. kinematic viscosity is considered some other significant features also evolve .The reduction of the value of kinematic viscosity results the change in nature of the waves from oscillatory shocks to periodic one.

Pankaj Kumar Mandal

Papers

The roles of non-extensivity and dust concentration as bifurcation parameters in dust-ion acoustic traveling waves in magnetized dusty plasma

Nonplanar ion-acoustic shocks in electron–positron–ion plasmas: Effect of superthermal electrons

Nonplanar ion-acoustic two-soliton systems in quantum electron–positron–ion plasmas

Cylindrical Zakharov–Kuznestov equation for ion-acoustic waves with electrons featuring non-extensive distribution

Zakharov–Kuznestov–Burger Equation for Ion-Acoustic Waves in Cylindrical Geometry