Ion-acoustic Waves In Plasma Research Articles

Effects of adiabaticity of electrons and negative ions on the modulational instability of ion-acoustic waves in electronegative plasma

In the present work, we investigate modulational instability (MI) in an unmagnetised collisionless electronegative plasma consisting of inertialess adiabatic electrons, inertialess adiabatic negative ions and mobile positive ions. For this purpose, a nonlinear Schrodinger equation (NLSE) is derived to study envelope evolution of the ion-acoustic carrier waves for our system by using reductive perturbation technique. In examining the stability/instability of the ion-acoustic envelope wavepackets, the critical wavenumber kc at which MI sets in is found to be shifted to higher values as adiabaticity γ increases. The effects of electron-to-negative ion temperature ratio σn and negative ion density fraction f on the region for propagation of stable wave pulses are also discussed. Within the instability region, the rational solution of NLSE provides the rogue wave (RW) profiles which is localised in space and time. With the increase of adiabaticity, the possibility for the formation of RW decreases at the lower wavenumber which is in good agreement with experimental observations. The change in adiabaticity significantly influences the rogue wave amplitudes. Maximum pulse height for RW is found to be increasing with the increase of adiabaticity. Our theoretical findings may be helpful for basic characteristic study of rogue waves in the laboratory as well as space plasmas.

Three-dimensional dissipative ion-acoustic rogue waves in magnetized plasma with adiabatic ions and nonextensive electrons

ABSTRACT The modulational instability of ion-acoustic rogue waves in a three-dimensional magnetized, dissipative plasma consisting of inertial warm positive ions and nonextensive electrons has been theoretically investigated. Using the well-known reductive perturbation method, the (3+1)-dimensional modified nonlinear Schrödinger equation (mNLSE), i.e. the standard NLSE in addition to the dissipative term has been derived and then solved to obtained instability criteria, as well as first- and second-order rogue wave solutions. It is found that increasing viscosity results in dissipation of energy which makes the IARW shorter and thinner as was reported in the literature. Furthermore effects of relevant parameters such as nonextensive parameter, and magnetic field on growth rate and rogue waves solutions were discussed in detail. The results of the present investigation may be useful in understanding and predicting the nonlinear excitations that occur in space and laboratory dissipative plasma systems.

Stable soliton solutions to the shallow water waves and ion-acoustic waves in a plasma

The Kawahara equation (KE) and the modified Kawahara equation (MKE) are important modeling equations to interpret shallow water waves with surface tension, magneto-acoustic wave in plasma and gravity waves. In this study, the stable broad-ranging soliton solutions including the well-known bell-shape soliton, anti-bell shape soliton, periodic soliton, compacton, kink, etc. are established through the sine-Gordon expansion (SGE) method. The effect of the physical parameters, namely the dispersion and perturbed dispersive coefficients in the surface elevation are shown through the figure. The surface elevations remain ascertainable for diverse values of the physical and the associated free parameters. The 3D and contour plot of the ascertained solutions clarifies the surface wave properties. The achieved results for each modeling equation provide a significant contribution in analyzing the ion-acoustic waves in plasma, gravity waves, the surface waves in shallow water. This study asserts that the SGE method is reliable, competent, easy and powerful for extracting closed form soliton solutions.

The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution* *Project supported by the National Natural Science Foundation of China (Grant No. 11975143), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2018MA017), the Taishan Scholars Program of Shandong Province, China (Grant No. ts20190936), and the Shandong University of Science

The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied. First, we design a new disturbance expansion to describe the ion fluid velocity and electric field potential. It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation. Then, based on the piecewise function perturbation, a (3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov (mKdV-ZK) equation is derived for the first time, which is an extended form of the classical mKdV equation and the ZK equation. The (3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle. Obviously, it is more accurate to depict some complex plasma processes and phenomena. Further, the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed. Finally, using the multi-exponential function method, the non-resonant multiwave solutions are constructed, and the characteristics of ion-acoustic waves are well described.

Nonlinear dynamics of ion-acoustic waves in quantum plasmas with exchange-correlation effects

Abstract Nonlinear properties of ion-acoustic waves (IAWs) are studied in electron-ion (EI) degenerate plasma with the electron exchange-correlation effects by using the quantum hydrodynamic (QHD) model. To investigate arbitrary amplitude IAWs, we have reduced the model equations into a system of ordinary differential equations using a traveling wave transformation. Computational investigations have been performed to examine the combined effect of Bohm potential and exchange-correlation potential significantly modifies the dynamics of IAWs by employing the concept of dynamical systems. The equilibrium points of the model are determined and its stability natures are analyzed. The phase portrait and Poincaré return map of the dynamical system are displayed numerically. Quasiperiodic as well as chaotic dynamics of the system are confirmed through the Poincaré return map diagrams.

On the long-wave approximation for the Euler-Poisson system

We study the long wave approximation to the Euler-Poisson system for the ion-acoustic wave in cold plasma according to the spatial-temporal scale and the amplitude of waves. We first justify rigorously that in the long-wave limit, the one-way propagating solutions of the Euler-Poisson system are well approximated by the unidirectional solutions of the Burgers-or KdV equation with responding to the different parameter scales. We then demonstrate that the solutions could be convergent to two wave packets in opposite directions, where each wave packet involves independently as a solution of the Burgers-or KdV equation.

Dynamical properties of nonlinear ion-acoustic waves based on the nonlinear Schrödinger equation in a multi-pair nonextensive plasma

Abstract Dynamical properties of nonlinear ion-acoustic waves (IAWs) in multi-pair plasmas (MPPs) constituting adiabatic ion fluids of positive and negative charges, and q-nonextensive electrons and positrons are examined. The nonlinear Schrödinger equation (NLSE) is considered to study the dynamics of IAWs in a nonextensive MPP system. Bifurcation of the dynamical system obtained from the NLSE shows that the system supports various wave forms such as, nonlinear periodic wave, kink and anti-kink waves in different ranges of q. The analytical solutions for ion-acoustic nonlinear periodic wave, kink and anti-kink waves are obtained. The impacts of system parameters such as, nonextensive parameter (q), mass ratio of negative and positive ions (μ 1), number density ratio of positive and negative ions (μ 2), number density ratio of positrons and negative ions (μ p), temperature ratio of positive ions and electrons (σ 2) and temperature ratio of electrons and positrons (δ) on IAW solutions are bestowed. The results of this study are applicable to understand different dynamical behaviors of nonlinear IAWs found in the Earth’s ionosphere, such as, D-region [H+, O 2 − ${\mathrm{O}}_{2}^{-}$ ] and F-region [H+, H−] and multipair plasma system laboratory [C+, C−].

Nonlinear periodic coupled Alfvén and ion-acoustic wave structures in plasmas

The nonlinear propagation of coupled Alfvén and ion-acoustic waves is investigated in homogeneous, magnetized and collisionless electron-ion plasma. The ion parallel motion is included in the model so that ion-acoustic wave couples with Alfvén wave in plasmas. In linear limit, the dispersion relation of coupled Alfvén and ion-acoustic waves is derived and its dispersion effects are investigated analytically as well as numerically using laboratory plasma parameters, given in the literature. Using reductive perturbation method, the Korteweg–de Vries (KdV) equation is derived for nonlinear coupled Alfvén and ion-acoustic waves in plasmas by applying appropriate periodic boundary conditions. The cnoidal wave solution of coupled Alfvén and ion-acoustic waves in terms of Jacobian elliptic function (cn) is obtained and its soliton solution is also investigated. The numerical plots of cnoidal wave and soliton structures with variations of plasma β (defined as the ratio of kinetic pressure to magnetic pressure) and obliqueness of the wave propagation with respect to external magnetic field are presented for illustration. It is found that low amplitude compressive structures of nonlinear coupled Alfvén and ion-acoustic waves exist in a magnetized plasma, which moves with sub-Alfvénic wave speed.

Dynamics of ion-acoustic waves in nonrelativistic magnetized multi-ion quantum plasma: the role of trapped electrons

The presented work provides a new perspective of quantum nonlinear propagation of ion-acoustic (IA) waves in a magnetized collisionless and dissipative multi-ion plasma system, composed of cold positive and negative charged nonrelativistic ions, negatively charged immobile heavy ions and trapped electrons; all existed in a quantizing magnetic field. We address the reductive perturbation method to derive the Korteweg-de Vries- Burgers (KdV-Burgers) and modified KdV-Burgers equations. The bifurcation theory of planar dynamical systems is applied to investigate the existence of the solitary wave and the periodic traveling wave solutions of the resulting mKdV-Burgers equation. Accordingly, the phase portrait topology is illustrated for this equation. To study the nonlinear waves in case of mKdV- Burgers, we obtain some interesting physical solutions for mKdV- Burgers. These solutions are in the form of soliton, a combination between the shock and the soliton, and finally monotonic and oscillatory shock waves. Only rarefactive IA waves are obtained for the slow mode of phase velocity. It is found that the IA solitons, IA shocks are affected by the plasma system parameters. The presented theoretical research can be successfully implemented to understanding the solitary and shocks structures in dense magnetized quantum plasmas such as those existing in white dwarfs and in the intense-laser plasma interactions.

Ion-acoustic compressive and rarefactive solitary waves in unmagnetised plasmas with positrons and two-temperature superthermal electrons

Ion-acoustic solitary waves (IASWs) in plasma consisting of ions, positrons and superthermal electrons in two distinct temperatures have been studied. The reductive perturbation method (RPM) has been employed to derive the Korteweg–de Vries and modified KdV equation. Numerical and analytical studies show that compressive and rarefactive solitons exist for the selected parametric range depending on the spectral indexes, $$\kappa $$ $$(\kappa _{h,} \kappa _{c} )$$ and their respective densities $$(\nu ,\mu )$$ . It is found that spectral indexes $$(\kappa _{h,} \kappa _{c})$$ and their relative densities have significant impact on the basic properties, i.e., amplitude and width as well as on the nature of IASWs. Variations of amplitude and width for the compressive and rarefactive solitary waves have been analysed graphically with different plasma parameters like spectral indexes of cold and hot electrons $$(k_{c} ,k_{h}),$$ their respective densities, ionic temperature ratio, positron temperature ratio as well as with the temperature ratio of the two-electron species. The amplitude of the compressive (rarefactive) solitary waves increases (decreases) on increasing $$k_{h}$$ . However, the amplitude of the compressive (rarefactive) solitary waves decreases (increases) on increasing $$k_{c}$$ . The investigations of such solitary waves may be helpful for the critical understanding of space where superthermal electrons with two different temperatures exist along with positrons and ions (e.g. Saturn’s magnetosphere, pulsar magnetosphere).

Various localized nonlinear wave structures in the (2 + 1)-dimensional KdV system

Korteweg–de-Vries (KdV) equation has many applications such as in the description of shallow water waves and ion-acoustic waves in plasmas. In this paper, we investigate the novel nonlinear wave structures in the [Formula: see text]-dimensional KdV system. Starting from the [Formula: see text]-soliton solution of the [Formula: see text]-dimensional KdV system, some new interaction phenomena of line soliton, breather soliton and lump soliton are found based on the Hirota bilinear method and the long wave limit method. The interaction processes of such solutions are shown graphically to display the novel nonlinear structures in this system. These interesting phenomena in this work could be helpful for understanding certain physical phenomena in nonlinear optics and relevant fields.

Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas

In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speedλ, electron number density (throughβ3) and the fractional orderα,β,ωon the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.

Exact Solution for the Zakhrov-Kuzentsov Equation by Adomian Decomposition Method

The Zakharov-kuznetsov equation (ZK-equation) governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and not isothermal electrons in the presence of a uniform magnetic field. This equation is a nonlinear equation. The main objective in this paper is to find an exact solution of ZK-equation using Adomain decomposition method. An exact solution of ZK(n,n,n) is derived by Adomain decomposition method. The solution of types ZK(2,2,2) and ZK(3,3,3) are presented in many examples to show the ability and efficiency of the method for ZK-equation. The solution is calculated in the form of convergent power series with easily computable components.

Improved $\tan \left (\frac {\Phi (\xi )}{2}\right )$-Expansion Approach for Burgers Equation in Nonlinear Dynamical Model of Ion Acoustic Waves

The main purpose of this research is to find new and more exact traveling wave solutions of nonlinear dynamical model of ion acoustic waves in plasma with the help of famous reductive perturbation technique. A well-known nonlinear evolution equation, namely Burgers equation, is derived to investigate ion acoustic waves in relativistic plasma containing electrons and positrons. The traveling wave solution of Burgers equation is carried out by an affective integration tool, namely improved $\tan \left (\frac {\Phi (\xi )}{2}\right )$ expansion method. As a result, different types of solutions such as periodic, kink, rational, exponential function, and hyperbolic function, are obtained. The wave profiles of solitary wave solutions are graphically depicted. The algorithm of the suggested technique is also outlined. It is admitted that the used method is efficient and influential tool for constructing solitary wave solutions of nonlinear evolution equations.

A novel approach for nonlinear equations occurs in ion acoustic waves in plasma with Mittag-Leffler law

Purpose The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM). Design/methodology/approach The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator. Findings The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. Originality/value To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

Three-dimensional modified Korteweg-de Vries equation in a magnetised relativistic plasma with positron beam and vortex-like electron distribution

The nonlinear features of Ion Acoustic (IA) waves are studied in a fully relativistic three-dimensional (3-D) plasma system with consideration of effect of both positron beam and trapped electrons. We consider a set of 3-D magnetised hydrodynamic equations with pressure expansion for our plasma model along with kinetic Vlasov equation for electrons. Applying the perturbative expansion technique, a Modified Korteweg-de Vries (m-KdV)-like equation is derived, exhibiting the evolution of small amplitude IA waves in plasma. The modified coefficient of nonlinear term in K-dV equation has arrived due to impact of vortex-like distribution of electrons. An analytical and numerical investigation of the nonlinear evolution equations is exhibited with external magnetic field effects, the time derivative pressure expansion as well as other parameters like relativistic effect, mass variation, beam velocity and temperature effect have been taken into consideration. The presence of vortex like trapped electron distribution and positron beam governs the influence of soliton structure quite significantly. The present result should help us to understand the experiments that involve particle trapping and also the salient features of astrophysical environment like ionospheric plasma together with situations in plasma describing the electrostatic solitary structures usually seen in antimatter-related environment in interplanetary region.

Reduction in the $$\mathbf {(4+1)}$$-dimensional Fokas equation and their solutions

An integrable extension of the Kadomtsev–Petviashvili (KP) and Davey–Stewartson (DS) equations is investigated in this paper. We will refer to this integrable extension as the $$(4+1)$$-dimensional Fokas equation. The determinant expressions of soliton, breather, rational, and semi-rational solutions of the $$(4+1)$$-dimensional Fokas equation are constructed based on the Hirota’s bilinear method and the KP hierarchy reduction method. The complex dynamics of these new exact solutions are shown in both three-dimensional plots and two-dimensional contour plots. Interestingly, the patterns of obtained high-order lumps are similar to those of rogue waves in the $$(1+1)$$-dimensions by choosing different values of the free parameters of the model. Furthermore, three kinds of new semi-rational solutions are presented and the classification of lump fission and fusion processes is also discussed. Additionally, we give a new way to obtain rational and semi-rational solutions of $$(3+1)$$-dimensional KP equation by reducing the solutions of the $$(4+1)$$-dimensional Fokas equation. All these results show that the $$(4+1)$$-dimensional Fokas equation is a meaningful multidimensional extension of the KP and DS equations. The obtained results might be useful in diverse fields such as hydrodynamics, nonlinear optics, and photonics, ion-acoustic waves in plasmas, matter waves in Bose–Einstein condensates, and sound waves in ferromagnetic media.

Dynamics of optical solitons and conservation laws of a new (2+1)-dimensional integrable nonlinear evolution equation in deep water oceanic waves

An integrable extension of the famous Schrödinger equation in (2[Formula: see text]+[Formula: see text]1) dimension, named Kundu–Mukherjee–Naskar (KMN) equation, governing the evolution of ion-acoustic wave in magnetized plasma and oceanic rogue waves is considered, and dark/black as well as gray optical soliton solutions are constructed by using a complex envelope ansatz approach with appropriate conditions for the existence of solitons. Also, a new class of combined gray and black optical soliton solutions is obtained by applying Chupin Liu’s theorem, and it is found to be anti-dark solitons. Additionally, Gaussian wave solutions are derived. Further, the investigation of symmetry analysis, nonlinear self-adjointness and conservation laws (Cls) for the KMN equation are carried out. These results further enrich and deepen the understanding of the dynamics of a higher-dimensional soliton propagation.

Nonlinear Theory of Backward and Oblique Ion-Acoustic Waves in Plasma with Unidirectionally Moving Ions

Oblique ion-acoustic waves in plasma with unidirectionally moving ions are considered. Within the framework of the linear theory, a two-dimensional dispersion relation is derived and the occurrence of backward and sideward waves in the system is demonstrated. The nonlinear theory of backward and sideward waves developed in this study is based on derivation and analysis of Sagdeev’s pseudopotential. The nonlinear profiles of backward and sideward ion-acoustic waves were calculated. It was found that backward and sideward waves are undistinguishable in their profiles from a regular forward ion-acoustic wave.

Bifurcation analysis of ion-acoustic waves in an adiabatic trapped electron and warm ion plasma

Bifurcation analysis of ion-acoustic waves in complex plasmas in the presence of adiabatic trapped electrons and warm ions is studied. Using bifurcation theory of dynamical structure, the Hamiltonian system inculpated electrostatic potential is derived. Effects of physical parameters, such as T and , are shown on the analytical solitary wave solution. The numerical results show that parameters T and affect significantly on nonlinear electrostatic solitary waves. By adding an external periodic perturbation to unperturbed Hamiltonian system, we investigate quasiperiodic structure of the perturbed Hamiltonian system.