Acoustic Wave Solutions Research Articles

Existence of both compressional and rarefactive nonlinear solitary waves in a chain of dust particles

Not only the compressional dust acoustic solitary wave, but also the rarefactive one in a chain of the dust particles are verified by using the molecular dynamics simulation method. The compressional dust acoustic solitary wave is also obtained by using the traditional reductive perturbation method, while the rarefactive dust acoustic solitary wave solution is fitted by the numerical simulation results. The application scope of the traditional reductive perturbation method to derive compressional dust acoustic solitary waves in a chain of the dust particles is given. The application scope of the fitted results of the rarefactive dust acoustic solitary waves is also given.

Amplitude reflections and interaction solutions of linear and nonlinear acoustic waves with hard and soft boundaries

In this study, the propagation of a fundamental plane mode in a bifurcated waveguide structure with soft–hard boundaries is analyzed by using the Helmholtz equation. The explicit solution is given to this bifurcated spaced waveguide problem by means of matching the potential across the boundary of continuity. Amplitudes of the reflected field in all those regions have been evaluated, and the energy balance has been derived. We have observed the reflection of the acoustic wave against the wavenumber and shown its variation with the duct width. Convergence of the problem has been shown graphically. In our analysis, we notice that the reflected amplitude decreases as the duct spacing increases; as a result, the acoustic energy will increase as the duct spacing increases. It is expected that our analysis could be helpful to give better understanding of wave reflection in an exhaust duct system. We then reduce the linear acoustic wave equation to the Kadomtsev–Petviashvili (KP) equation. Multiple-periodic wave interaction solutions of the KP nonlinear wave equation are investigated, and the energy transfer mechanism between the primary and higher harmonics is explained, which, to the best of our knowledge, is overlooked.

Dust-acoustic solitary wave solutions for mixed nonlinearity modified Korteweg-de Vries dynamical equation via analytical mathematical methods

In the recent work, our purpose to study the dust acoustic solitary wave (DASWs) for mixed nonlinearity mKdV equation under dusty plasma. The constructed new results denote to dust acoustic solitary wave solutions for mixed nonlinearity mKdV equation under dusty plasma by proposed two analytical techniques. The determined solutions symbolize to antikink-kink, bright-dark solitons, and periodic solitary waves. The physical interpretation for determined solutions is represented by two-dim and three-dim graphically by symbolic computation to know the different phenomena for DASWs. The analysis for mixed nonlinearity modified models proved that suggested techniques are efficient ad powerful for analytical research other non-linear PDEs.

Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean

Waves propagate in a free-surface ocean due to compressibility and gravity (and surface tension at much smaller scale). Analytical solutions have long been derived independently for acoustic and gravity waves, i.e., acoustic waves or internal-gravity waves in an unbounded ocean, surface-gravity waves in a free-surface-ocean, and acoustic or internal modes in a bounded ocean. In the present study, surface tension and earth-rotation are neglected and a simple, unified model based on inner and boundary dispersion relations is derived for waves propagating in a compressible, stratified, free-surface ocean. Branches of acoustic gravity wave solutions are identified and visually analysed in phase-space. Taylor developments are then carried out with respect to small parameters describing stratification and compressibility and are compared with numerical approximations of the intersection of inner and boundary dispersion surfaces. Finally, the model recovers the known approximations for swell, long-surface waves, internal-gravity waves, internal modes, acoustic waves or acoustic modes, and also provides information on the modifications of these solutions due to stratification and compressibility and on the coupling of acoustic and gravity waves. Two peculiar regions of the acoustic-gravity wave phase-space are more specifically highlighted and studied in detail: one for long waves shedding new light on the distinction between surface waves and low-order internal modes, the other for marginally stable surface waves of intermediate length-scale.

Bending of pinned dust-ion acoustic solitary waves in presence of charged space debris.

We consider a low temperature plasma environment in the low Earth orbital region in the presence of charged space debris particles. The dynamics of (2+1)-dimensional nonlinear dust-ion acoustic waves with weak transverse perturbation, generated in the system, is found to be governed by a forced Kadomtsev-Petviashvili equation, where the forcing term depends on charged space debris function. The bending phenomena of some exact dust-ion acoustic solitary wave solutions in the x-t and x-y planes are shown; they result from the consideration of different types of possible localized debris functions. A family of exact pinned accelerated solitary wave solutions has been obtained where the velocity changes over time but the amplitude remains constant. The shape of the debris function also changes during its propagation. Also, a special exact solitary wave solution has been derived for the dust-ion acoustic wave that gets curved in spatial dimensions with the curvature depending upon the nature of the forcing debris function. Such intricate solitary wave solutions may be useful in modeling real experimental data.

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.

Symmetry reduction, conservation laws and acoustic wave solutions for the extended Zakharov–Kuznetsov dynamical model arising in a dust plasma

In this article, we consider the extended Zakharov–Kuznetsov (EZK) equation, which describes the nonlinear plasma dust acoustic waves (DAWs) in a magnetized dusty plasma. Dusty plasmas consist of three components: electrons, highly negatively charged dust grains, and two-temperature ions (low-temperature ions and high-temperature ions). We study the Lie symmetries, reductions, conservation laws and new exact solutions of EZK equations. Conservation laws for EZK equation is derived by applying the new conservation theorem of Ibragimov. Similarity solution for EZK equation will be obtained using Lie symmetry method. We find the Lie symmetries group of EZK equation, using similarity variables, get reduction equation, solving the reduction equations and then get the similarity solution. Solitary wave solutions of the EZK equation are derived from the reduction equation. Thus, some new exact explicit solutions of the EZK equation are obtained.

Propagation of Ion-Acoustic Solitary Waves for Damped Forced Zakharov Kuznetsov Equation in a Relativistic Rotating Magnetized Electron-Positron-Ion Plasma

The purpose of this paper is to determine the nonlinear properties of the ion-acoustic solitary waves (IASW) propagating obliquely, under the influence of external periodic force combining with a damping term in a rotating, weakly relativistic and magnetized electron-positron-ion plasma. Reductive perturbation technique is employed to derive the damped forced Zakharov Kuznetsov (DFZK) equation. Using the momentum conservation law, ion acoustic solitary wave solution is obtained for DFZK equation. Considerable effects are found in the structures of IASW with the variation of the ratio of temperature of electron and positron, concentration of positron, obliqueness, relativity, ion temperature, magnetic field and due to the presence of external forces. Numerical simulations are depicted for clear vision of the propagating properties of IASW.

Interaction of electron acoustic waves in the presence of superthermal electrons in terrestrial magnetosphere

We have investigated the propagation and interaction of nonlinear electron acoustic waves (EAWs) in a plasma comprising hot (superthermal) and cold electrons and immobile ions. We have derived the Korteweg-de Vries equation for EAWs in the small amplitude limit. Employing the Hirota's Direct method, we have investigated the multisoliton solutions for electron acoustic solitary waves (EASWs). It has been found that the system under consideration admits only rarefactive electrostatic solitary structures. As the observable data are available in terms of electric field rather than electric potential, therefore, we have discussed our results in terms of bipolar electric field structures. The numerical analysis has revealed that the ratio of hot to cold electrons and superthermality of hot electrons play a crucial role in changing the amplitude of EASWs. The interaction of the two solitons and its dependence on the choice of propagation vectors, superthermality, and density ratio have also been elaborated. The results of the present study may be beneficial to comprehend the interaction between two EASWs in astrophysical and laboratory plasmas.

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.

Fast surface acoustic wave solution method based on the generalized Green’s function

The characteristics of generalized Green’s function elements with different materials and cuts are analyzed. The real part has only one zero crossing point that corresponds to a free surface acoustic wave (SAW) when the imaginary part of elements H33 is zero. Moreover, the signs of the real part on two sides of the zero crossing point are opposite. A fast SAW solution algorithm is developed on the basis of the characteristics of H33. Free surface SAW velocity vf is obtained by searching the zero crossing point of H33, and metal surface SAW velocity vm is obtained by searching the zero crossing point of an effective permittivity that is smaller than vf. A numerical simulation is performed. Results show that the obtained SAW velocity and electromechanical coupling coefficients are consistent with the reported results. Moreover, the calculation time of the proposed SAW solution method is approximately 10% of the existing methods, which verify its feasibility.

Nonplanar dust acoustic solitary and rogue waves in an ion beam plasma with superthermal electrons and ions

The propagation characteristics of dust acoustic solitary and rogue waves are investigated in an unmagnetized ion beam plasma with electrons and ions following kappa-type distribution in nonplanar geometry. The reductive perturbation method (RPM) is employed to derive the cylindrical/spherical Korteweg–de Vries (KdV) equation, which is further transformed into standard KdV equation by neglecting the geometrical effects. Using new stretching coordinates, nonlinear Schrödinger equation (NLSE) has been derived from the standard KdV equation to study the different order rational solutions of dust acoustic rogue waves (DARWs). The impact of various physical parameters on the characteristics of dust acoustic solitary waves (DASWs) is elaborated specifically in nonplanar geometry. Further, the effects of ion beam and superthermality of electrons/ions on the characteristics of DARWs are studied. The results obtained in the present investigation may be useful in comprehending a variety of phenomena in Earth’s magnetosphere polar cap region where the presence of positive ion beam has been detected and also in other regions of space/astrophysical environments where dust along with superthermal electrons and ions exists.

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.

Analytical electron acoustic solitary wave solution for the forced KdV equation in superthermal plasmas

Analytical electron acoustic solitary wave (EASW) solution is investigated in the presence of periodic force for an unmagnetized plasma consisting of cold electron fluid, superthermal hot electrons, and stationary ions. Employing the reductive perturbation technique, the forced Korteg-de Vries (KdV) equation is derived for electron acoustic waves. For the first time, an analytical solution for EASWs is derived in the presence of periodic force. The effects of the ratio between hot electron and cold electron number densities at equilibrium (α), spectral index (κ), speed of the traveling wave (M), strength (f0), and frequency (ω) of the periodic force are studied on the analytical solution of EASWs. It is observed that the parameters α, κ, M, f0, and ω affect significantly the structures of the electron acoustic solitary waves. The results may have relevance in laboratory plasmas as well as in space plasma environments.

Efficient boundary integral solution for acoustic wave scattering by irregular surfaces

The left–right operator splitting method is studied for the efficient calculation of acoustic fields scattered by arbitrary rough surfaces. Here, the governing boundary integral is written as a sum of left- and right-going components, and the solution expressed as an iterative series, expanding about the predominant direction of propagation. Calculation of each term is computationally inexpensive both in time and memory, and the field is often accurately captured using one or two terms. The convergence and accuracy are examined by comparison with exact solution for smaller problems, and a series of much larger problems are tackled. The method is also immediately applicable to other scatterers such as waveguides, of which examples are given.

Qualitative analysis of the positron-acoustic waves in electron-positron-ion plasmas with κ deformed Kaniadakis distributed electrons and hot positrons

Qualitative analysis of the positron acoustic (PA) waves in a four-component plasma system consisting of static positive ions, mobile cold positron, and Kaniadakis distributed hot positrons and electrons is investigated. Using the reductive perturbation technique, the Korteweg-de Vries (K-dV) equation and the modified KdV equation are derived for the PA waves. Variations of the total energy of the conservative systems corresponding to the KdV and mKdV equations are presented. Applying numerical computations, effect of parameter (κ), number density ratio (μ1) of electrons to ions and number density (μ2) of hot positrons to ions, and speed (U) of the traveling wave are discussed on the positron acoustic solitary wave solutions of the KdV and mKdV equations. Furthermore, it is found that the parameter κ has no effect on the solitary wave solution of the KdV equation, whereas it has significant effect on the solitary wave solution of the modified KdV equation. Considering an external periodic perturbation, the perturbed dynamical systems corresponding to the KdV and mKdV equations are analyzed by employing three dimensional phase portrait analysis, time series analysis, and Poincare section. Chaotic motions of the perturbed PA waves occur through the quasiperiodic route to chaos.

Nonlinear excitations for the positron acoustic waves in auroral acceleration regions

Positron acoustic waves (PAWs) in an unmagnetized electron-positron-ion (e-p-i) plasma consisting of mobile cold positrons, immobile positive ions, q-nonextensive distributed electrons and hot positrons are studied. The standard reductive perturbation technique (RPT) is applied to derive the Kurteweg-de Vries (KdV) and modified Kurteweg-de Vries (mKdV) equations for PAWs. Variations of the total energy of the conservative systems corresponding to the KdV and mKdV equations are presented. Using numerical simulations, effect of the nonextensive parameter (q), temperature ratio (σ) of electrons to hot positrons and speed (U) of the traveling wave are discussed on the positron acoustic solitary wave solutions of the KdV and mKdV equations. Considering an external periodic perturbation, the perturbed dynamical systems corresponding to the KdV and mKdV equations are analyzed by employing phase orbit analysis, Poincare section and Lyapunov exponent. The frequency (ω) of the external periodic perturbation plays the role of the switching parameter in chaotic motions of the perturbed PAWs through quasiperiodic route to chaos. This work may be useful to understand the qualitative changes in the dynamics of nonlinear perturbations in auroral acceleration regions.

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

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.

Existence and stability of alternative dust ion acoustic solitary wave solution of the combined MKP-KP equation in nonthermal plasma

The aim of this paper is to extend the recent work of Sardar et al. [Phys. Plasmas 23, 073703 (2016)] on the stability of the small amplitude dust ion acoustic solitary wave in a collisionless unmagnetized nonthermal plasma in the presence of isothermal positrons. Sardar et al. [Phys. Plasmas 23, 073703 (2016)] have derived a KP (Kadomtsev Petviashvili) equation to study the stability of the dust ion acoustic solitary wave when the weak dependence of the spatial coordinates perpendicular to the direction of propagation of the wave is taken into account. They have also derived a modified KP (MKP) equation to investigate the stability of the dust ion acoustic solitary wave when the coefficient of the nonlinear term of the KP equation vanishes. When the coefficient of the nonlinear term of the KP equation is close to zero, a combined MKP-KP equation more efficiently describes the nonlinear behaviour of the dust ion acoustic wave. This equation is derived in the present paper. The alternative solitary wave solution of the combined MKP-KP equation having profile different from sech2 or sech is obtained. This alternative solitary wave solution of the combined MKP-KP equation is stable at the lowest order of the wave number. It is found that this alternative solitary wave solution of the combined MKP-KP equation and its lowest order stability analysis are exactly same as those of the solitary wave solution of the MKP equation when the coefficient of the nonlinear term of the KP equation tends to zero.

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.