Acoustic Rogue Waves Research Articles

Dust-ion acoustic rogue waves in six-component dusty plasma

In this work, we investigate the modulational instability of finite amplitude dust-ion acoustic nonlinear waves in a six-component cometary dusty plasma. Such plasma system is composed of Oxygen ion-pair, negative dust particles, kappa distributed light ions of Hydrogen, solar electrons and cometary electrons of the comet tail. By employing the standard reductive perturbation technique, a nonlinear Schrödinger-type equation is obtained. This equation governs the investigation of the modulational instability of finite amplitude dust-ion acoustic nonlinear waves. Our analysis shows two parametric domains, where the dust-ion acoustic waves are modulationally stable and unstable depending on the plasma configurational parameters. Within the unstable domain, rogue waves could be generated due to the nonlinear and dispersion properties of plasma system. The effects of some relevant plasma parameters on the profile of rogue waves are studied. The obtained results might be useful for better understanding the modulational instability of nonlinear plasma waves and formation of dust-ion acoustic rogue waves in space plasmas.

B<i>Ä</i>CKLUND TRANSFORMATIONS AND ROUGE WAVES IN THE FRAME OF A FRACTIONAL ORDER MODEL IN MAGNETIZED DUSTY PLASMA

<abstract> Dusty plasma has become a hot topic in physics in recent years because of its wide application in the space environment, industrial processing and fusion reaction. The (3+1)-dimensional modified Zakharov-Kuznetsov (mZK) equation describing waves propagation in dusty plasma is derived via the reduced perturbation method, based on the governing equation. Furthermore, integer-order equation is derived as the fractional modified Zakharov-Kuznetsov (TF-mZK) equation. The exact solution and B$ \ddot{a} $cklund transformation are obtained by the fractional transformation and Bell polynomials. Finally, the rouge wave phenomenon in magnetized dusty plasma is described, and the effects of fractional order, phase velocity and dust-cyclotron frequency on the propagation characteristics of dust acoustic rogue waves are analyzed. </abstract>

Formation of ion acoustic rogue waves in warm dense matter

Formation of ion acoustic rogue waves in warm dense matter

Three-dimensional modulational instability of dust acoustic waves in the presence of generalized (r, q) distributed electrons

A three-dimensional (3D) modulational instability (MI) of dust acoustic waves (DAWs) in a three-component magnetized dusty plasma system consisting of a negatively charged fluid, inertialess generalized (r, q) distributed electrons and Boltzmann distributed ions, is investigated. The basic system of the nonlinear hydrodynamic equations is reduced to a 3D nonlinear Schrödinger equation (NLS) which is valid for small but finite amplitude DAWs using a reductive perturbation technique. The domain of the stability and instability regions is investigated that is strongly affected by the spectral parameters of the generalized (r, q) distribution and the electron-to-ion temperature ratio (T e /T i ). The existence domains for observing the first-and second-order solutions of the dust acoustic rogue waves (DARWs) are determined and the basic features (viz the width and amplitude) for the first-order solution are found to be significantly dependent on the system physical parameters changes such as T e /T i , number density ratio [n e0/(n d0 z d0)] and the dust cyclotron frequency (ω cd ) as well as the spectral indexes r and q. A comparison between the first-and second-order DARW amplitudes is presented. Moreover, another comparison between the first-order DARW amplitudes obtained by generalized (r, q) distributed electrons and those corresponds to Maxwellian is provided. Finally, implication of our consequences in specific plasma situations are briefly discussed.

Head-on collision of ion-acoustic multi-solitons and study of rogue waves in electron-beam superthermal plasma

In this investigation, head-on collision of ion-acoustic (IA) multi-solitons and study of characteristics of ion acoustic rogue waves in an unmagnetized plasma which includes ion fluid, superthermal hot electrons, and penetrated by electron beam have been presented. The Korteweg-de Vries equation have been derived by employing the extended Poincaré-Lighthill-Kuo (PLK) method. Further, multi-solitons of different KdV equations have also been determined by following the Hirota bilinear method. The combined effects of electron beam parameters and variation of different physical parameters on the characteristics of IA solitons and phase shifts of multi-solitons have been analyzed. It is remarked that electron beam components and other plasma parameters significantly influence the phase shifts and other properties of ion-acoustic solitons (IASs). Furthermore, the nonlinear Schrodinger equation (NLSE) has been derived from the KdV equation by using appropriate transformation. The characteristics of different orders rogue waves have also been studied from the different solutions of NLSE. The results of this study may be of great importance to understand the characteristics properties of various kinds of nonlinear solitary structures in different kinds of plasma systems.

Nonlinear ion acoustic rogue waves in a superthermal electron–positron–ion plasma

In this paper, the nonlinear ion acoustic rogue waves (IARWs) are investigated in an unmagnetized, collisionless plasma which consist of positive ions, superthermal electrons and positrons, respectively. A nonlinear Schrodinger equation (NLSE) of IAW packets has been obtained by using the reductive perturbation technique. Furthermore, the effects of superthermal electrons and positrons on the nonlinear dispersion relation, the group velocity and the modulational instability of nonlinear ion acoustic wave (IAW) packets have been studied in detail. At the same time, the characteristics of first- and second-order IARW also have been discussed. It seems that there is some significant influence of superthermal electrons and positrons on the nonlinear ion acoustic waves. Meanwhile, it is also found that the first- and second-order IARW consisting of Peregrine breathers can be excited by using the modulational instability in this system.

Dust acoustic rogue waves of fractional-order model in dusty plasma

In this paper, the fractional-order model is used to study dust acoustic rogue waves in dusty plasma. Firstly, based on control equations, the multi-scale analysis and reduced perturbation method are used to derive the (3+1)-dimensional modified Kadomtsev–Petviashvili (MKP) equation. Secondly, using the semi-inverse method and the fractional variation principle, the (3+1)-dimensional time-fractional modified Kadomtsev–Petviashvili (TF-MKP) equation is derived. Then, the Riemann–Liouville fractional derivative is used to study the symmetric property and conservation laws of the (3+1)-dimensional TF-MKP equation. Finally, the exact solution of the (3+1)-dimensional TF-MKP equation is obtained by using fractional order transformations and the definition and properties of Bell polynomials. Based on the obtained solution, we analyze and discuss dust acoustic rogue waves in dusty plasma.

Heavy ion–acoustic rogue waves in magnetized electron–positron multi‐ion plasmas

AbstractNon‐linear heavy ion‐acoustic waves (HIAWs) are studied in a homogeneous magnetized four‐component multi‐ion plasma composed of inertial heavy negative ions, light positive ions, and inertia‐less non‐extensive electrons and positrons. The non‐linear Schrödinger equation is derived in this model using the perturbation method. The criteria for modulational instability of HIAWs and the basic features of finite‐amplitude heavy ion acoustic rogue waves (HIARWs) are investigated. The presence of the magnetic field was found to reduce the amplitude of HIARWs and enhances the stability. It is interesting to note that increasing positive ion mass causes decreases in the amplitude and width of rogue waves, which is opposite behaviour to that demonstrated in the previous study of these waves in an unmagnetized plasma. Furthermore, it is also shown that striking parameters, such as the non‐extensive parameter, the positron number density, the electron number density, the electron temperature, and the magnetic field parameter, play an undeniable role on the stability of waves packets. The findings of the present investigation may be of wide relevance to some plasma environments, such as active galactic nuclei, pulsar magnetospheres, and other magnetic confinement systems.

The evolution of rogue wave triplets and super rogue waves in superthermal polarized space dusty plasma

This present investigation has been instigated to examine the impact of polarization force on modulational instability of dust acoustic (DA) waves and transition of rogue wave triplets to super rogue waves in dusty plasma composed of negative dust as fluid, Boltzmannian electrons, and superthermal ions. The presence of superthermal ions has remarkably altered the impact of polarization force. An increment in ion superthermality index restricts the polarization parameter toward smaller values. By adopting the reductive perturbation technique, the nonlinear Schrödinger equation (NLSE) is procured that determines the modulational instability of the dust acoustic waves. It is observed that the effect of polarization force is constricted by the wavenumber domain in the advent of the instability region. The rational solution of NLSE describes the evolution of dust acoustic rogue wave triplets, which further transform into the super rogue waves by means of superposition of triplets. It is remarked that the amalgamation of polarization force and superthermal ions have an explicit impact on the characteristics of different kinds of dust acoustic rogue waves. It is intensified that our present theoretical pronouncements may shed light on the salient features of different kinds of DA rogue waves in laboratory experiments and space/astrophysical regions, especially in Saturn's magnetosphere, planetary rings, and comet tails, etc.

Phononic rogue waves

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schroedinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue wave like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.

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.

The characters of ion acoustic rogue waves in nonextensive plasma

Several well-known nonlinear waves in the rational solutions of the nonlinear Schrödinger equation are studied in two-component plasmas consisting of ions fluid and nonextensive electrons, such as Kuznetsov–Ma breather (K-M), bright soliton, rogue wave (RW), Akhmediev breather (AB) and dark soliton, and so on. In this paper, we have investigated the characteristics of K-M, AB, and RW's propagation in plasma with nonextensive electron distribution, and the dependence of amplitude and width for ion acoustic rogue waves in this system. It is found that K-M' triplet is appearance-disappearance-appearance-disappearance. AB solitons only appear once and RW is a single wave that appears from nowhere and then disappears. It is also noted that the wave number and nonextensive parameter of electrons have a significant influence on the maximum envelope amplitude, but, the influence of the width was not significant. At the same time, the effects of the small parameter, which represent the nonlinear strength, on the amplitude and width of ion acoustic rogue waves are also being highlighted.

Head-on collision between two dust acoustic solitary waves and study of rogue waves in multicomponent dusty plasma

In this investigation, the study of head-on collision between two dust acoustic solitary waves (DASWs) and characteristics of rogue waves in a dusty plasma composed of dust fluid, kappa distributed ions, electrons, and positrons has been presented. Two Korteweg-de Vries equations are derived by employing the extended Poincaré–Lighthill–Kuo reductive perturbation method. The analytical phase shifts and trajectories after head-on collision of two DA solitary waves have been studied numerically. It is found that the presence of superthermal ions, electrons, as well as positrons; concentrations of electrons and positrons; and temperature of electrons and dust have an emphatic influence on the phase shifts after the head-on collision of two rarefactive DA solitary waves. The time evolution of two rarefactive DASWs has also been presented. Further, the generation of dust acoustic rogue waves (DARWs) has been studied in the framework of rational solution of nonlinear Schrödinger equation. The dependence of the rogue wave profile on the relevant physical parameters has been discussed in detail. It is emphasized that the real implementation of our present results may be of great importance in different regions of space and astrophysical environments, especially in the interstellar medium and Jupiter rings.

The impact of positrons beam on the propagation of super freak waves in electron-positron-ion plasmas

In this work, we examine the nonlinear propagation of planar ion-acoustic freak waves in an unmagnetized plasma consisting of cold positive ions and superthermal electrons subjected to cold positrons beam. For this purpose, the reductive perturbation method is used to derive a nonlinear Schrödinger equation (NLSE) for the evolution of electrostatic potential wave. We determine the domain of the plasma parameters where the rogue waves exist. The effect of the positron beam on the modulational instability of the ion-acoustic rogue waves is discussed. It is found that the region of the modulational stability is enhanced with the increase of positron beam speed and positron population. Second as positrons beam increases the nonlinearities of the plasma system, large amplitude ion acoustic rogue waves are pointed out. The present results will be helpful in providing a good fit between the theoretical analysis and real applications in future laboratory plasma experiments.

Generation of acoustic rogue waves in dusty plasmas through three-dimensional particle focusing by distorted waveforms

Rogue waves have been observed in fluids and other wave contexts. Experiments now show the formation of 3D acoustic rogue waves in dusty plasmas; they result from wave–particle interactions driving the dust particles into high-amplitude dynamics. Rogue waves—rare uncertainly emerging localized events with large amplitudes—have been experimentally observed in many nonlinear wave phenomena, such as water waves1,2,3,4,5,6, optical waves7,8, second sound in superfluid He II (ref. 9) and ion acoustic waves in plasmas10. Past studies have mainly focused on one-dimensional (1D) wave behaviour through modulation instabilities1,3,4,5,7,11, and to a lesser extent on higher-dimensional behaviour5,6,8,11,12. The question whether rogue waves also exist in nonlinear 3D acoustic-type plasma waves, the kinetic origin of their formation and their correlation with surrounding 3D waveforms are unexplored fundamental issues. Here we report the direct experimental observation of dust acoustic rogue waves in dusty plasmas and construct a picture of 3D particle focusing by the surrounding tilted and ruptured wave crests, associated with the higher probability of low-amplitude holes for rogue-wave generation.

Nonlinear dust acoustic rogue waves in a two temperature charged dusty grains plasma

The properties of nonlinear dust-acoustic rogue waves in an unmagnetized, collisionless, four-component dusty plasma system consisting of electrons, nonthermal ions, hot and cold dust species have been investigated. The basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of the rogue wave properties on the ion energetic population parameter is discussed. The results of the present investigation could be applicable in Saturn F-ring.

Dust ion acoustic rogue waves in superthermal warm ion plasma

The properties of dust ion acoustic rogue waves (DIARWs) in an unmagnetized collisionless plasma system composed of charged dust grains, superthermal electrons and warm ions as a fluid are studied. The multiple scale perturbation method is used to derive a nonlinear Schrödinger equation (NLSE) for DIARWs. From the coefficients of nonlinearity and dispersion, we have determined the critical wave number threshold kcr at which modulational instability sets in. This critical wave number depends on the various plasma parameters, viz. superthermality of electrons, ion temperature and dust concentration. Within the modulational instability region, a random perturbation of amplitude grows and thus, creates DIARWs. It is found that DIARWs are significantly affected by electron superthermality (via κ), ion temperature (via σ) and dust concentration (via f). In view of the crucial importance of DIARWs in space environments, our results may be useful in understanding the basic features of DIARWs that may occur in space plasmas.

Effect of nonextensive electron and ion on dust acoustic rogue waves in dusty plasma of opposite polarity

Propagation of nonlinear dust-acoustic waves in a magnetized collisionless plasma having positively, negatively charged dust grains and nonextensive distributed electrons and ions has been investigated. A reductive perturbation method is used to obtain a nonlinear Korteweg-de Vries (KdV) equation describing the model. The dynamics of the modulational instability gives rise to the formation of rogue waves that is described by a nonlinear Schrodinger equation. The dependence of rogue waves profiles on positive and negative charged dust cyclotron frequencies, nonextensive parameters of electrons and ions is investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as cometary tails and upper mesosphere.

Electrostatic rogue waves in a plasma with a relativistic electron beam

AbstractThe properties of nonlinear electrostatic acoustic rogue waves in a three-component plasma composed of electron, positron, and relativistic electron beam are investigated. The reductive perturbation method is used to obtain a Korteweg–de Vries equation. The dynamics of the modulationally unstable wave packets described by the Korteweg–de Vries equation gives rise to the formation of rogue pulses that is described by a nonlinear Schrödinger equation for small wave number. The effects of physical parameters on the profile of rogue waves are investigated numerically. The electrostatic rogue waves, as predicted here, may be associated with the nonlinear structures caused by the interaction of relativistic jets with plasma medium, such as in the active galactic nuclei and in the magnetosphere of collapsing stars.