Quantum Ion-acoustic Waves Research Articles

On the convergence of the solution for a reduced model of the vectorial quantum Zakharov system

In this paper, we study the limit behavior of the smooth solution for a reduced vectorial quantum Zakharov system which describes the interaction between the quantum Langmuir waves and quantum ion-acoustic waves in the plasmas. We first give the local existence and uniqueness of the solution to the quantum Zakharov system. Then we derive the uniform bounds of solution with appropriate initial data, and prove that the solution of the quantum Zakharov system converges to the solution of the nonlinear Schrödinger system.

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

Propagation of small-amplitude quantum ion-acoustic waves and its fractal representations is investigated in an electron-ion quantum plasma with separated spin electrons in the framework of the KdV and EKdV equations derived using reductive perturbation technique. These two equations are transformed into planar dynamical systems by using suitable traveling wave transformation. Qualitatively different phase portraits of these two systems are drawn with their respective Sagdeev’s pseudopotential curves and surface plots. Distinct orbits in the phase portraits give rise to distinct wave solutions. Periodic and superperiodic wave solutions are investigated numerically and solitary wave solutions are derived analytically. The effect of parameters such as Mach number, direction cosine, spin polarization and frequency ratio on these wave solutions are presented. For instance, it is seen that the spin density polarization ratio has an impressive effect on the amplitude of the wave solution, while the frequency ratio has no effect on its amplitude. Also, we have provided a physical explanation for our finding. Further, the dynamical features of the original system and reconstructed system using fractal interpolation function are investigated under the external forcing term. Chaotic and quasiperiodic phenomena are observed for different initial conditions. The results may help to better understand the degenerate electron gas that exists in dense astrophysical bodies.

Nonlinear and supernonlinear ion-acoustic wave phenomena in an electron-positron-pair-ion quantum plasma

A four-component quantum plasma consisting of electrons, positrons, negative heavy ions and positive light ions is proposed in this work. The dynamics of nonlinear and supernonlinear ion-acoustic waves are studied in the framework of the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations which are derived employing the reductive perturbation technique. Using Galilean transformation these two evolution equations are transformed into planar dynamical systems. All possible phase portraits and corresponding small-amplitude Sagdeev's pseudopotential of these dynamical systems are presented graphically. The unique topology of phase portrait and a maxima in between two minimas in pseudopotential curves clearly establish quantum ion-acoustic superperiodic waves. Solitary, periodic and superperiodic wave solutions corresponding respectively to homoclinic, periodic and superperiodic orbits in phase portraits are obtained numerically and the influence of different parameters on these waves is observed. Further, various kinds of analytical wave solutions for the two evolution equations are discussed.

Analytical solutions for the (3＋1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation in plasma physics

In the current study, we investigate the (3＋1)-dimensional extended quantum Zakharov–Kuznetsov equation through two different methods namely the sine–Gordon expansion method and the (1∕G′)-expansion method. The given model represent the nonlinear propagation of the quantum ion-acoustic wave. Traveling wave transformation has been used, in order to convert the governing equation into a non-linear ordinary differential equation. As a result, we successfully construct various exact wave solutions, such as shock, topological, non-topological solutions, periodic wave solutions, and singular solutions. In addition, 2D, 3D and contour surfaces are plotted according to the appropriate parameters values.

Multistability and dynamical properties of ion-acoustic wave for the nonlinear Schrödinger equation in an electron–ion quantum plasma

Multistability and dynamical properties of quantum ion-acoustic (QIA) waves are examined in a quantum plasma consisting of warm ions and inertialess electrons. Using phase plane analysis, QIA periodic, a pair of solitonic and superperiodic wave solutions are reported. The physical parameters viz., ion–electron Fermi temperature ratio (ρ), quantum parameter (H), travelling wave velocity (V) and β affect significantly on these wave solutions. Considering an external periodic perturbation various types of QIA coexisting hidden attractors (periodic, quasiperiodic and chaotic attractors) are observed in parametric space through phase plots, time series plots and Lyapunov exponents. Coexisting QIA hidden attractors are reported for the first time in electron–ion quantum plasmas.

Bifurcation analysis of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation in a dense quantum plasma

Bifurcations of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation are examined in a dense quantum (DQ) plasma comprising of positive ions, electrons and positrons utilizing reductive perturbation technique (RPT) and the concept of dynamical system for the first time. Using RPT and travelling wave transformation, the model equations are converted to a dynamical system. Existence of kink, anti-kink and periodic wave solutions is shown through phase plot and time series plot based on suitable parametric conditions on coefficient of viscosity ($$\eta $$), density ratio of electrons and ions ($$\mu $$) and wave velocity (V). Depending on different parameters, variation of anti-kink, kink and periodic waves is depicted through numerical simulation. The periodic wave of the Burgers equation due to the periodic orbit is offered for the first time in plasmas through Jacobi elliptic function. It is seen that physical parameters $$\eta ,~\mu $$ and V significantly influence amplitude and smoothness of the kink, anti-kink and periodic wave profiles. The output of this contribution may be utilized to interpret the bifurcation behaviour of periodic, kink and anti-kink waves in DQ plasmas with viscosity effect.

Dynamical behaviour of non‐linear quantum ion acoustic wave in weakly magnetized electron–positron–ion plasma

AbstractIn order to investigate the propagation characteristics of linear and non‐linear ion acoustic waves (IAWs) in electron–positron–ion quantum plasma in the presence of external weak magnetic field, we have used a quantum hydrodynamic model, and degenerate statistics for the electrons and positrons are taken into account. It is found that the linear dispersion relation of the IAW was modified by the externally applied magnetic field. By using the reductive perturbation technique, a gyration‐modified Korteweg‐de Vries equation is derived for finite amplitude non‐linear IAWs. Time‐dependent numerical simulation shows the formation of an oscillating tail in front of the ion acoustic solitons in the presence of a weak magnetic field. It is also seen that the amplitude and width of solitons and oscillating tails are affected by the relevant plasma parameters such as quantum diffraction, positron concentration, and magnetic field. We have performed our analysis by extending it to account for approximate soliton solution by asymptotic perturbation technique and non‐linear analysis via a dynamical system approach. The analytical results show the distortion of the shape of the localized soliton with time, and the non‐linear analysis confirms the generation of oscillating tails.

On the effect of fractional statistics on quantum ion acoustic waves

In this paper, I study the effect of a small deviation from the Fermi–Dirac statistics on the quantum ion acoustic waves. For this purpose, a quantum hydrodynamic model is developed based on the Polychronakos statistics, which allows for a smooth interpolation between the Fermi and Bose limits, passing through the case of classical particles. The model includes the effect of pressure as well as quantum diffraction effects through the Bohm potential. The equation of state for electrons obeying fractional statistics is obtained and the effect of fractional statistics on the kinetic energy and the coupling parameter is analyzed. Through the model, the effect of fractional statistics on the quantum ion acoustic waves is highlighted, exploring both linear and weakly nonlinear regimes. It is found that fractional statistics enhance the amplitude and diminish the width of the quantum ion acoustic waves. Furthermore, it is shown that a small deviation from the Fermi–Dirac statistics can modify the type structures, from bright to dark soliton. All known results of fully degenerate and non-degenerate cases are reproduced in the proper limits.

Impact of electron exchange-correlation on drift acoustic solitary waves

The impact of electron exchange-correlation term on the linear and nonlinear quantum ion (QIA) acoustic drift waves in a highly degenerate plasma is investigated. An analytical approach is employed to derive the differential equation which is later on turned into Sagdeev energy integral equation that can be utilized to get drift solitons under existence conditions. It is noted that phase speed/frequency of the linear drift quantum ion acoustic (QIA) waves increases with electron exchange-correlation effect, but the amplitude of the corresponding solitons decreases with inclusion of these effects. Present study is carried out with reference to highly dense plasma environments like fast ignition inertial confinement fusion and white dwarfs etc.

New exact periodic elliptic wave solutions for extended quantum Zakharov–Kuznetsov equation

In this paper, the exact solutions of extended quantum Zakharov–Kuznetsov (QZK) equation which arises in hydrodynamic that describe the nonlinear propagation of the quantum ion-acoustic waves have been procured. The trial equation method with the discrimination system of polynomials is employed to find the analytical solutions. The local time fractional derivative is used in place of ordinary derivatives to get fractional model. Some plentiful new exact traveling wave solutions of nonlinear extended QZK equation are constructed. The solutions consist of singular, Jacobi elliptic and dark soliton solutions. Furthermore, the constraint conditions for the existence of these solutions are also presented.

Nonlinear quantum ion acoustic shock wave dynamics with exchange-correlation effects

The dynamics of linear and nonlinear electrostatic shock excitations is studied in homogeneous, unmagnetized, unbounded and dissipative quantum plasma consisting of electrons and ions. The dissipation in the system is taken into account by incorporating the ion kinematic viscosity. The system is modelled using the quantum hydrodynamic equations in which the electrons are significantly affected by the quantum forces, viz., the quantum statistical pressure, the quantum Bohm potential and electron exchange-correlations due to electron spin. In the weakly nonlinear limit, using reductive perturbation method deformed Korteweg-de Vries Burgers’s (KdVB) equation, which elegantly combines the effects of nonlinearity, dispersion and dissipation is derived. It is found that the present model predicts the existence of both nonlinear oscillatory and monotonic shock structures. The temporal evolution, stability and phase-space dynamics of nonlinear ion acoustic shocks are investigated numerically to elucidate the effects of quantum diffraction, electron exchange correlation and ion kinematic viscosity.

On the standing waves of quantum Zakharov system

In this work, we study the quantum Zakharov system which describes the nonlinear interaction between high-frequency quantum Langmuir waves and low-frequency quantum ion-acoustic waves. We show the existence and the stability of the standing waves of quantum Zakharov system for the spacial dimensions d=1,2,3.

Peakons and new exact solitary wave solutions of extended quantum Zakharov-Kuznetsov equation

In this paper, the three dimensional extended quantum Zakharov-Kuznetsov equation, which arises in the dimensionless hydrodynamic equations describing the nonlinear propagation of the quantum ion-acoustic waves, is investigated by an auxiliary equation method. As a result, peakons and a series of new exact traveling wave solutions, including bell-shaped, kink-type solitary wave, shock wave, periodic wave, and Jacobi elliptic solutions, are obtained. We also analyze the three kinds of nonlinear structures of our results, i.e., blowup, peakons, and shock wave. These new exact solutions will enrich the previous results and help us to further understand the physical structures and analyze the nonlinear propagation of the quantum ion-acoustic waves.

On one dimensional quantum Zakharov system

In this paper, we discuss the properties of one dimensional quantum Zakharov system which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic waves. The system with initial data $(E(0),n(0),\partial_t n(0))\in H^k\bigoplus H^l\bigoplus H^{l-2}$ is local well posedness in low regularity spaces. Especially, the low regularity result for $k$ satisfies $-3/4<k\leq -1/4$ is obtained by using the key observation that the convoluted phase function is convex and careful bilinear analysis. The result can not be obtained by using only Strichartz inequalities for "Schr\"{o}dinger" waves.

Investigations about the characteristic behavior of the linear mode of quantum acoustic waves ion

The dispersion relation of linear quantum ion acoustic waves is derivate according to a fluid approach that depends on the kinetic description of the systems of charged particles model. We discussed the dispersion relation by changing its parameters and graphically represented. We found through graphs that there is full agreement with previous studies on the subject of interest. That motivates us to discuss the dispersion relation of waves depending on the original basic parameters that implicitly involved in the relationship which change the relationship by one way or another, such as electron Fermi temperature and the density at equilibrium state.

Quantum Ion-Acoustic Oscillations in Single-Walled Carbon Nanotubes

Abstract Quantum ion-acoustic oscillations in single-walled carbon nanotubes are studied by employing a quantum hydrodynamics model. The dispersion equation is obtained by Fourier transformation, which exhibits the existence of quantum ion-acoustic wave affected by change of density balance due to presence of positive or negative heavy species as stationary ion clusters and wave potential at equilibrium. The numerical results are presented, and the role of quantum degeneracy, nanotube geometry, electron exchange-correlation effects, and concentration and polarity of heavy species on wave dispersion is pointed out for typical systems of interest.

Investigations about the characteristic behavior of the linear mode of quantum acoustic waves ion

The dispersion relation of linear quantum ion acoustic waves is derivate according to a fluid approach that depends on the kinetic description of the systems of charged particles model. We discussed the dispersion relation by changing its parameters and graphically represented. We found through graphs that there is full agreement with previous studies on the subject of interest. That motivates us to discuss the dispersion relation of waves depending on the original basic parameters that implicitly involved in the relationship which change the relationship by one way or another, such as electron Fermi temperature and the density at equilibrium state.

Nonplanar KdV and KP equations for quantum electron–positron–ion plasma

Nonlinear quantum ion-acoustic waves with the effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the standard reductive perturbation technique, a cylindrical Kadomtsev–Petviashvili equation for ion-acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave are studied analytically. It is found that the dynamics of ion-acoustic solitary waves (IASWs) is governed by a three-dimensional cylindrical Kadomtsev–Petviashvili equation (CKPE). The results could help in a theoretical analysis of astrophysical and laser produced plasmas.

Quantum ion-acoustic wave oscillations on a quantum plasma half-space

We investigate the dispersion properties of surface quantum ion-acoustic wave oscillations on an electron–ion quantum plasma half-space, taking into account the quantum diffraction effects. We deduce the perturbed electron density by using the linearized quantum fluid model, while the ion density perturbation is obtained by the classical theory. We derive an analytical dispersion relation for the surface waves of the system with low-frequency, by applying the Poisson equation as well as the appropriate boundary conditions. We use the dimensionless parameter H, proportional to quantum tunneling effects and show the system support linear quantum ion-acoustic waves, where in the limit of small H, the classical ion-acoustic waves emerge.

Quantum ion-acoustic wave oscillations in metallic nanowires

The low-frequency electrostatic waves in metallic nanowires are studied using the quantum hydrodynamic model, in which the electron and ion components of the system are regarded as a two-species quantum plasma system. The Poisson equation as well as appropriate quantum boundary conditions give the analytical expressions of dispersion relations of the surface and bulk quantum ion-acoustic wave oscillations.