Nonlinear Ion Acoustic Solitary Waves Research Articles

Nonlinear ion-acoustic waves with Landau damping in non-Maxwellian space plasmas

The dynamics of nonlinear ion-acoustic solitary waves in the presence of kinetic (Landau type) damping have been investigated in a collisionless, non-magnetized electron-ion plasma. A cold ion fluid model, coupled to a Vlasov-type kinetic equation for the electron dynamics, has been adopted as a starting point. The electron population was assumed to be in a kappa-distributed state, in account of the non-Maxwellian behavior of energetic (suprathermal) electrons often observed in Space. A multiscale perturbation technique has led to an evolution equation for the electrostatic potential, in the form of a modified Korteweg-de Vries (KdV) equation, incorporating a non-local term accounting for Landau damping (associated with the electron statistics). Exact analytical solutions have been obtained, representing solitary waves undergoing amplitude decay over time. The combined effect of Landau damping and non-Maxwellian electron statistics (via the kappa parameter) on the characteristics of IASWs has been examined. Numerical integration of the evolution equation has been undertaken, to elucidate the importance of kinetic Landau damping on a shock-shaped initial condition. The results of this investigation aim to improve our understanding of the dynamics of nonlinear electrostatic waves under the influence of Landau damping in various space plasma environments.

On the dynamics of soliton interactions in the stellar environments

The effects of trapping of relativistically degenerate electrons are studied on the formation and interaction of nonlinear ion-acoustic solitary waves (IASWs) in quantum plasmas. These plasmas are detected in high-density astrophysical entities and can be created in the laboratory by interacting powerful lasers with matter. The formula for the number density of electrons in a state of relativistic degeneracy is provided, along with an analysis of the non-relativistic and ultra-relativistic scenarios. While previous studies have delved into specific aspects of relativistic effects, there needs to be a more detailed and systematic examination of the fully relativistic limit, which is essential for gaining a holistic perspective on the behavior of solitons in these extreme conditions. The aim of this work is to comprehensively investigate the fully relativistic limit of the system to fill this gap. The reductive perturbation technique is utilized to deduce the Korteweg–de Vries (KdV) equation, which is used to analyze the properties of the IASWs. Hirota bilinear formalism is applied to obtain single- and multi-soliton solutions for the KdV equation. The numerical analysis is focused on the plasma properties of the white dwarf in the ongoing investigation. The amplitude of the IASWs is found to be maximum for the non-relativistic, intermediate for the ultra-relativistic, and minimum for the fully relativistic limit. Most importantly, it is found that the fastest interaction occurs in the non-relativistic limit and the slowest in the fully relativistic limit.

The (1+1)-dimensional nonlinear ion acoustic waves in multicomponent plasma containing kappa electrons

Large amplitude (1+1)-dimensional nonlinear ion acoustic waves are theoretically studied in multicomponent plasma consisting of positively charged ions and negatively charged ions, ion beam, kappa-distributed electrons, and dust grains, respectively. By using the Sagdeev potential method, the dynamical system and the Sagdeev potential function are obtained. The important influences of system parameters on the phase diagram of this system are investigated. It is found that the linear waves, the nonlinear waves and the solitary waves are coexistent in the multicomponent plasma system. Meanwhile, the variations of Sagdeev potential with parameter can also be obtained. Finally, it seems that the propagating characteristics of (1+1)-dimensional nonlinear ion acoustic solitary waves and ion acoustic nonlinear shock wave can be influenced by different parameters of this system.

Higher-order nonlinear dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

Higher-order nonlinear dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

Large amplitude electrostatic solitary waves in anisotropic plasma

The propagation of nonlinear ion-acoustic solitary waves (IASWs) is investigated in a magnetized anisotropic electron ion plasma with Cairns distributed electrons. The ions are warm and exhibit pressure anisotropy due to the external magnetic field. The energy integral equation for the wave potential is derived via Sagdeev approach. The effect of various physical plasma parameters (nonthermality, ion pressure anisotropy) on the characteristics of IASWs is investigated in detail. The present investigation could be of interest to space and astrophysical plasma systems having ion pressure anisotropy, for instance, in the magnetosphere and near earth magnetosheath.

Analytical study of ion-acoustic solitary waves in a magnetized plasma with degenerate electrons

The propagation of fully nonlinear ion acoustic solitary waves (IASW) in a magneto-plasma with degenerate electrons was investigated by Abdelsalam et al. [[1] Physics Letters A 372 (2008) 4923]. Based on their work in the present work, a rigorous and general analytical study is presented. This confirms their implied assumption that (i) only hump and no cavity is possible and (ii) for humps, the algebraic equation for the maximum density N obtained by them determines it uniquely (naturally assumes N > 1). Here we confirm analytically their assertion that N decreases with lx (the direction cosine of the wave vector k along the x-axis) and N increases with the increase of the Mach number (M).

Modeling of nonlinear ion-acoustic solitary, snoidal and superperiodic wave phenomena due to ionospheric escape of Venus

Solar wind induces the escape of ions from the ionospheric shell of an unmagnetized planet, Venus. To analyze the dynamics of ions due to the escape process, the modeling of ion-acoustic waves (IAWs) is scrutinized for an interaction between an upper ionospheric plasma of Venus constituting mobile electrons with two kinds of positive ions, viz, H+ and O+ and the solar-wind which is composed of highly energized electrons and protons. The Sagdeev pseudopotential is examined for wave breaking phenomena. Employing the concept of phase plane analysis, the formulated autonomous dynamical systems are examined for all feasible nonlinear and supernonlinear periodic waves. To support the existence of nonlinear and supernonlinear waves, the graph of the total energy function is plotted in three-dimensional space. A typical set of Venusian plasma parameters are used to discuss the analytical solutions of the dynamical system by the method of Jacobi elliptic function. Effect of traveling wave velocity on the plot of the total energy function and the wave solutions are discussed.

Nonlinear ion acoustic solitary wave in collisional pair ion plasma with trapped electrons

Nonlinear ion acoustic solitary wave in collisional pair ion plasma with trapped electrons

Ion-acoustic Gardner solitons in negative ion plasmas

The ion-acoustic Gardner solitons in negative ion plasma have been studied. The Gardner equation is deduced by employing the reductive perturbation technique. We have investigated the ion-acoustic Gardner solitons in negative ion plasma in the parametric regime where the KdV equation is no longer valid to study soliton solution. It is found that for a given set of parameter values with negative ion concentration ( α ) less than the critical value ( α c ), i.e. α < α c ; the system supports compressive Gardner soliton, whereas for α > α c , rarefactive Gardner soliton exists. It is also investigated that Gardner solitons exist only for the fast mode, whereas no such structure is found in the case of the slow mode. The present study may be helpful to understand the nonlinear ion-acoustic solitary waves in space plasma and laboratory experiment plasmas also can be helpful for the study of Ionospheric auroral and magnetospheric plasmas where negative ions are present.

Nonlinear rarefactive isothermal ion acoustic waves in magnetized ultrarelativistic degenerate plasmas

Abstract Nonlinear rarefactive isothermal ion-acoustic periodic travelling waves (RIIAPTWs) are examined in a magnetized ultrarelativistic degenerate plasma, containing warm fluid ions and ultrarelativistic degenerate inertialess electrons as well as positrons and immobile heavy negative ions. In the linear regime, the excitation of an isothermal ion-acoustic mode and its evolution are investigated. The physical behavior of nonlinear rarefactive isothermal ion-acoustic waves (RIIAWs) in this plasma model is governed by a Zakharov–Kuznetsov (ZK) equation. The analytical solutions for the nonlinear rarefactive isothermal ion-acoustic solitary waves (RIIASWs) and RIIAPTWs are performed by the bifurcation analysis. A careful discussion demonstrates the excitations of RIIASWs and RIIAPTWs are amplified (i.e., the amplitudes become deeper), as the chemical potential (or the Fermi energy at zero temperature) of electrons is decreased. It is found physically that the presence of the ultrarelativistic degenerate positrons and stationary heavy negative ions have strong effects on features of nonlinear RIIASWs and RIIAPTWs. The implications of the present finding in compact astrophysical objects, such as white dwarf stars, have been discussed.

Ion acoustic waves in the dayside of Titan ionosphere: effect of the solar wind

We investigate the nonlinear ion-acoustic solitary waves for a plasma model at Titan's ionosphere dayside. The plasma system composed of three positive ions, namely HCNH⁺, C₂H₅⁺, and CH₅⁺, isothermal electrons and streaming solar wind particles (i.e. protons and electrons). The dynamics of the ion-acoustic waves is described by Korteweg de-Vries (KdV) equation. The analysis has been done by using a reductive perturbation method. The solitary wave solution is obtained and the effects of solar wind parameters on the pulses profile are examined. Furthermore, the effects of the relevant physical parameters on the profiles of soliton waves are investigated. It is found that only positive pulses are existing and there is not any negative pulses. The soliton amplitude increases with the increase of the phase velocity λ and the relative density protons-to-HCNH⁺. Also, it was found that the pulses decrease with the increase of the relative density C₂H₅⁺-to-HCNH⁺ and temperature ratio protons-to-electrons.

On the interaction of nonlinear ion acoustic solitary waves in non-ideal plasma incorporated with Cairns-Gurevich distributed electrons

A rigorous theoretical study of the head-on collision (HoC) of two ion acoustic solitons in unmagnetized non-ideal plasmas containing warm fluid ions and Cairns-Gurevich distributed electrons is presented. The extended Poincare-Lighthill-Kuo (PLK) method is employed and coupled modified Kortweg-de Vries (mKdV) equations describing the system are derived. The nonlinear evolution equations for the colliding solitons, the corresponding phase shifts and trajectories of the two solitary waves are calculated and analyzed numerically. It is found that the process of solitons collision strongly depends on the hybrid nonthermal trapped electron parameter. Shortly, it is detected that the collision phase shifts increase with the increment of the nonthermal parameter in the case of ideal plasma. Though, for ideal plasma case, the phase shifts are constant and larger than that of non-ideal case. The gained results could be useful in clarifying the requisite features of localized electrostatic disturbance in the Earth’s magnetosphere where such distribution exists.

Nonlinear ion acoustic solitary waves with dynamical behaviours in the relativistic plasmas

This work investigates the basic features of Nonlinear Ion Acoustic Solitary waves (NIASWs) and their dynamical behaviours in an unmagnetized relativistic collisionless plasma system via the Schamel Korteweg-de Vries (SKdV) equation. Such plasma is composed by the generalized distributed electrons, Boltzmann distributed positrons and relativistic warm ions. The influences of plasma parameters on NIASWs and their dynamical behaviours are investigated by comparing 26−term expansion of relativistic Lorentz factor (RLF) with both of weakly (2−term expansion of RLF) and highly (3−term expansion of RLF) regimes. It is found that the 26−term expansion of RLF are significantly changed NIASWs instead of both weakly and highly relativistic regimes. Therefore, the theoretical results would be very useful for understanding the nature (amplitude, width, polarity, etc.) of wave dynamics not only in astrophysical and space environments but also in further laboratory studies, where the proposed plasma assumptions are existed.

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.

Obliquely propagating nonlinear ion-acoustic solitary and cnoidal waves in nonrelativistic magnetized pair-ion plasma with superthermal electrons

The nonlinear propagation of ion-acoustic waves is considered in a magnetized system of collisionless and dissipative pair-ion plasma, composed of cold positively and negatively charged nonrelativistic ions, with superthermal electrons. obliquely propagating ion-acoustic solitary and cnoidal waves are investigated via a mechanical-motion analog Korteweg de Vries (KdV) approach. The characteristics of the emerged nonlinear magnetized waves are significantly modified by the effects of plasma parameters like the obliquity angle, superthermality parameter, negative to positive ions density ratio, electron density and it is also affected by the electron temperature. The obtained results can be generalized to be used to investigate the plasma waves nature in neutron stars, Saturn’s and Pulsars magnetospheres in addition to the laboratory plasmas.

Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics

In this article we studied analytically the propagation of nonlinear ion acoustic solitary waves modeled by the generalized Schamel (GS) equation arising in plasma physics using auxiliary equation mapping method. As a result, we found a series of more general and new families of solutions, which are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies and many other fields. The calculations prove that this method is more reliable, straightforward, and effective to study analytically other nonlinear complicated physical problems modeled by complex nonlinear partial differential equations arising in mathematical physics, hydrodynamics, fluid mechanics, mathematical biology, plasma physics, engineering disciplines, chemistry and many other natural sciences. We also have expressed our solutions graphically with the help of Mathematica 10.4 to understand physically the behavior of different shapes of ion acoustic solitary waves including kink-type, anti-kink-type, half-bright and dark soliton.

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.

Oblique propagation of solitary waves in weakly relativistic magnetized plasma with kappa distributed electrons in the presence of negative ions

The oblique propagation of nonlinear ion acoustic solitary waves (solitons) in magnetized collisionless and weakly relativistic plasma with positive and negative ions and super thermal electrons has been examined by using reduced perturbation method to obtain the Korteweg-de Vries equation that admits an obliquely propagating soliton solution. We have investigated the effects of plasma parameters like negative ion density, electrons temperature, angle between wave vector and magnetic field, ions velocity, and k (spectral index in kappa distribution) on the amplitude and width of solitary waves. It has been found out that four modes exist in our plasma model, but the analysis of the results showed that only two types of ion acoustic modes (fast and slow) exist in the plasma and in special cases only one mode could be propagated. The parameters of plasma for these two modes (or one mode) determine which one is rarefactive and which one is compressive. The main parameter is negative ions density (β) indicating which mode is compressive or rarefactive. The effects of the other plasma parameters on amplitude and width of the ion acoustic solitary waves have been studied. The main conclusion is that the effects of the plasma parameters on amplitude and width of the solitary wave strongly depend on the value of the negative ion density.

Large amplitude ion-acoustic solitons in warm negative ion plasmas with superthermal electrons

Large amplitude ion-acoustic solitons are investigated in a plasma consisting of warm adiabatic positive and negative-ions and hot superthermal electrons having kappa distributions. Using Pseudo-potential method an energy integral equation is derived for the system. The latter is analysed to examine the existence regions of the solitary waves. It is found that negative ion concentration (α), spectral index (k) and ionic temperature ratio (σ1 or σ2) significantly influence the characteristic of the solitons. Our numerical analysis shows that the system also supports rarefactive solitons for some selected set of plasma parameters. It is also found that large amplitude ion-acoustic compressive and rarefactive solitons exist simultaneously for the same values of plasma parameters. Further an increase in the superthermality (i.e. decreasing the value of spectral index k) leads to shrinking the existing domain of the large amplitude ion-acoustic solitons. The amplitude of the compressive/rarefactive solitons increases with the increase in negative ion concentration (α). Whereas, on increasing ionic temperature ratio (σ1 or σ2) the amplitude of the compressive/rarefactive soliton decreases. The effect of negative-ion concentration (α), temperature ratio of two ion species (σ1 and σ2), Mach number (M) and spectral index (k) on the characteristics of solitons are discussed in detail. The results of the present investigation may be helpful to understand the nonlinear ion-acoustic solitary waves in space plasma and laboratory plasmas, where two distinct groups of ions and non-Boltzmann distribution electrons are present.