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The nonlinear freak wave in electron–hole quantum GaAs semiconductor plasma is investigated via a nonlinear Schrödinger equation (NLS) equation. The latter contains the contributions of the electron and hole quantum recoil effects, quantum statistical pressures, as well as exchange and correlation effects. Typical values for GaAs semiconductor are used to estimate the profile of the nonlinear freak waves.

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... A number of different approaches have been proposed to explain and interpret the mystery about this type of waves. Indeed, the dynamics of RWs are closely related to the modulated envelope soliton creation and nonlinear breather induced by the modulational instability (MI) [21] . After a great deal of effort from researchers, they found that the closest approach to model the evolution of RWs in different nonlinear system is to study the MI of the modulated structures within one-dimensional/planar nonlinear Schrödinger equation (NLSE) [22,23] ...

... By substituting the values of ( f, g, h ) given in Eq. (21) and the RWs solution into Eq. (27) and by separating the real and imaginary parts, we get ...

The cylindrical rogue wave (RW) and breathers in a collisionless, unmagnetized, and warm pair-ion plasma having thermal electrons and stationary negatively dust grains are investigated. The derivative expansion technique (DET) is employed for reducing the fluid equations of the mentioned plasma model to a cylindrical nonlinear Schrödinger equation (CNLSE). Posteriorly, for investigating the characteristics features of the cylindrical modulated structures including cylindrical RW and breathers, the CNLSE is solved analytically and numerically via high-accurate ansatz and numerical methods. Some approximate (analytical and numerical) solutions to the CNLSE are obtained for the first time. The ansatz methods is employed for deriving some semi-analytical solutions with high-accuracy. Also, the hybrid method of lines and the moving boundary method (MOL-MBM) is employed for analyzing the CNLSE numerically. A comparison between the approximate analytical and numerical simulation solutions is carried out. Furthermore, the residual maximum global error for the obtained approximate solutions is estimated. We are absolutely sure that this study will help all researchers to understand the mechanism of propagating cylindrical wave in various fields of science such as plasma physics, fluid mechanics, optical fiber, nonlinear optics. etc.

... A number of different approaches have been proposed to explain and interpret the mystery about this type of waves. Indeed, the dynamics of RWs are closely related to the modulated envelope soliton creation and nonlinear breather induced by the modulational instability (MI) [21] . After a great deal of effort from researchers, they found that the closest approach to model the evolution of RWs in different nonlinear system is to study the MI of the modulated structures within one-dimensional/planar nonlinear Schrödinger equation (NLSE) [22,23] ...

... By substituting the values of ( f, g, h ) given in Eq. (21) and the RWs solution into Eq. (27) and by separating the real and imaginary parts, we get ...

In this work, some novel analytic traveling wave solutions including the cnoidal and solitary wave solutions of the planar Extended Kawahara equation are deduced. Four different analytical methods (the Jacobian elliptic function, Weierrtrass elliptic function, the traditional tanh method and the sech-square) are devoted for solving this equation. By means of the Jacobian elliptic function ansatz, the cnoidal and soliary wave solutions are obtained. Also, new cnoidal wave solutions are derived via a new hypothesis in the form of the Weierrtrass elliptic function. Moreover, the standard tanh method is utilized to get a new set of solitary wave solutions for the evolution equation. Over and above, the hyperbolic ansatz method (a new ansatz in the form of squre-sech) is employed to get a new set of solitary wave solutions for the evolution equation. Furthermore, all obtained solutions of the planar Extended Kawahara equation cover the traveling wave solutions of the planar modified Kawahara equation. These solutions maybe useful to many researchers interested in studying the propagation of nonlinear waves in nonlinear dispersion mediums like plasma physics, optical fibers, fluid mechanics, and many different branches of science.

... into equation (18) and taking into account the boundary conditions j 0 and We can now proceed analogously to the effect of electron beam parameters on the acoustic soliton profile and examine how the electron beam changes both the amplitude and width pulse. As can be seen from figure 2(a), increasing the electron beam streaming velocity leads to increasing the energy of the soliton pulse. ...

... Furthermore, it is convenient to combine equations(18) with(19) in order to have a new general evolution equation that represents the system in the vicinity of B ∼ O (ε) and at the critical values of the non- ...

This work treats the degrade of semiconductor lifetime during the pumping process. The criteria of nonlinear waves propagation that responsible for delivery the energy inside the semiconductor was determined. For this purpose, the quantum fluid model including the exchange-correlation potential, the Bohm potential, and the degenerate pressure is employed. The reductive perturbation theory is used to reduce the basic set of quantum hydrodynamic fluid equations to Korteweg-de Vries, modified Korteweg-de Vries, and Gardner equations. When the wave carrier frequency is much smaller than the frequency of hole plasma, the nonlinear rogue wave can exist and it is studied through the nonlinear Schrödinger equation. This study predicts the propagation of different nonlinear waves like a soliton, double layer, and rogue waves depending on the plasma and electron beam parameters. Thus, a practicable physical solution is introduced to avoid the generation of such energetic nonlinear waves during the pumping process.

... Recently, the super RW solutions in NLSE were studied theoretically and confirmed experimentally by many researchers [18,[65][66][67][68][69][70][71] . It is found that the super RWs can be treated as superpositions of several first-order/or fundamental RWs, and the superpositions can create higher amplitudes that still keep located both of time and space [71] . ...

... It is found that the super RWs can be treated as superpositions of several first-order/or fundamental RWs, and the superpositions can create higher amplitudes that still keep located both of time and space [71] . The super RW structures in different types of plasmas have been investigated in many articles [18,[66][67][68][69][70] . For any order, the RW solutions of the NLSE can be written in the following form ...

... Many researchers have investigated theoretically and experimentally the formulation of super freak waves in different environments [45][46][47]. These types of freak waves are formed when two or more first-order freak waves superimposed with each other. ...

In this investigation, the characteristics of ion acoustic (IA) solitary, breathers, and freak waves have been examined by using spin evolution quantum hydrodynamic model in a degenerate quantum plasma consisting of inertial non-degenerate ions and degenerate electrons with spin-up and spin-down states. The Korteweg–de Vries (KdV) equation is derived by employing reductive perturbation technique and its solution is determined to see the existence of IA solitary waves. Only positive potential solitary structures are formed. Further, using appropriate transformation, the KdV equation is transformed into nonlinear Schrödinger equation (NLSE) and its different order solutions are used to study the characteristics of breathers such as the Akhmediev breather, the Kuznetsov–Ma breather and freak waves. Further, the formation of super order of freak waves has also been explored. The influence of different plasma parameters including density polarization ratio has been investigated on the characteristics of IA solitary waves and different types of breathers. It is observed that the density polarization ratio has a strong influence on the characteristics of different types of nonlinear structures. The present investigation may be of great importance to provide physical insight to understand nonlinear dynamical processes in dense astrophysical regions such as white dwarfs and neutron stars.

... Whilst, Alfvén waves (AWs), which are lowfrequency electromagnetic waves, propagate along the direction of the magnetic field. Over several years, the significant characteristics of degenerate quantum plasmas encouraged investigators to examine the propagation of nonlinear waves in different configurations [2][3][4][5][6][7][8][9]. For degenerate quantum plasmas, the de Broglie thermal wavelength of the quantum charged particles is comparable to the characteristic spatial scales of the system. ...

Nonlinear propagation of monotonic and oscillatory magnetosonic shock waves in a magnetized degenerate quantum plasma consisting of ions and spin 1/2 nonrelativistic degenerate electrons is examined. The well-known reductive perturbation analysis is applied to obtain a Korteweg–de Vries–Burgers equation (KdVBE). The dissipative system of coupled nonlinear, ordinary, differential equations and the equilibrium points are hereby discussed on the basis of the bifurcation analysis. The nonlinear behaviour of shock wave structures is numerically investigated under the fourth order Runge-Kutta method. Numerical simulations show that the behaviour of monotonic and oscillatory magnetosonic shock waves depends essentially on the effects of quantum statistics and the spin magnetization energy. The present results may be helpful for an in-depth understanding of the nonlinear propagation of magnetosonic waves in magnetized degenerate quantum plasma, which occur in the dense astrophysical objects.

... In recent years, research on the pumping process of semiconductors has become very popular [9][10][11]. Much research on the quantum effects such as the electron/hole tunneling through a potential barrier (Bohm potential), and Fermi degenerate pressure which results from the high number density of the carrier charges has been done but they still lack [12][13][14][15][16][17][18][19][20][21][22][23]. ...

The degradation of quantum semiconductor plasma during electron pumping is an important problem since it has several applications in the technological industry. Moreover, the identification of such a problem cannot be accomplished by experiment alone and a further theoretical investigation is required. Owing to the energy gap of semiconductors, electrons should acquire energy in order to move from the valence band to the conduction band. Therefore, to employ the quantum fluid model that includes the exchange-correlation potentials, Bohm potential, and the degenerate pressure, the electron-hole lifetime should be greater than the plasma oscillation time. If the latter condition is not satisfied, the quantum fluid model failed to describe the system and it is convenient to use the density functional theory. As a result of that, we apply the quantum fluid model to GaN where the plasma oscillation has a time of 0.002 ps while the electron-hole lifetime is 1 ps. The modified Kadomtsev-Petviashvili (mKP) equation had been obtained using a new set of stretched coordinates as the Kadomtsev-Petviashvili (KP) equation had been derived in Ref. [1]. Our findings determine whether the quantum fluid model is valid or not in the case of semiconductor plasma. Studying exchange effects in a dynamic context has certain limitations. Thus, we stressed that the more accurate approaches introduced in the literature are hard to apply for nonlinear issues. Further, the applicability of our results is discussed, but not this much. Moreover, the numerical results showed that the electron beam parameters and quantum effects have significant effects on the growth of the solitary waves.

The propagation of electron-acoustic waves (EAWs) in an unmagnetized plasma, comprising (r,q)-distributed hot electrons, cold inertial electrons, and stationary positive ions, is investigated. Both the unmodulated and modulated EAWs, such as solitary waves, rogue waves (RWs), and breathers are discussed. The Sagdeev potential approach is employed to determine the existence domain of electron acoustic solitary structures and study the perfectly symmetric planar nonlinear unmodulated structures. Moreover, the nonlinear Schrödinger equation (NLSE) is derived and its modulated solutions, including first order RWs (Peregrine soliton), higher-order RWs (super RWs), and breathers (Akhmediev breathers and Kuznetsov–Ma soliton) are presented. The effects of plasma parameters and, in particular, the effects of spectral indices r and q, of distribution functions on the characteristics of both unmodulated and modulated EAWs, are examined in detail. In a limited cases, the (r,q) distribution is compared with Maxwellian and kappa distributions. The present investigation may be beneficial to comprehend and predict the modulated and unmodulated electron acoustic structures in laboratory and space plasmas.

In this study, the propagation mechanism of the unstable modulated structures (e.g., rogue wave (RW)) in the framework of the family of a Korteweg–de Vries (KdV) equation is discussed. Using the derivative expansion method, the KdV is converted to a nonlinear Schrödinger equation (NLSE); from now on, we refer to it as the KdV-NLSE. After that we shall discuss whether the KdV-NLSE is suitable for describing the rogue waves (RWs) or not. Also, we shall present some appropriate methods to discuss such waves in the event that the KdV-NLSE fails to describe them.

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.

In this paper, the dynamic responses of a Spar-type floating offshore wind turbine (FOWT) are simulated and analyzed under the scenarios with freak wave superimposed a uniform current. The wave-current interaction is considered in the process of freak wave generation. An improved phase modulation algorithm is used to generate the free surface profile of the freak wave. Compared with the deterministic wave modeling method, this method can realize the randomness of the sea state and also achieve high efficiency. The effect of the presence of current on the wave energy spectra is firstly investigated. Then the OC3 Hywind Spar-type FOWT in the parked condition is chosen as an example to study the dynamic responses under the extreme wave scenarios. An in-house MATLAB code based on a nonlinear aero-hydro-mooring coupled model is adopted to perform these numerical investigations. The simulations are conducted in the time domain and then the results of wave forces and platform motions in the surge, heave and pitch are summarized and analyzed considering the presence of current with different velocities. The results of mooring lines tension and the acceleration at nacelle are also investigated. Through the simulation results, we can have a clear understanding of the mechanism of the wave-current interaction phenomenon for extremely high waves in Gaussian seas. Furthermore, it also allows identifying the severest wave conditions which are important for the analysis of the floating structure ultimate design conditions.

Investigations of the nonlinear excitation and collisions of electrostatic solitons in a dense semiconductor plasma composed of electrons and holes are improved by using the higher-order corrections. Applying the extended Poincaré-Lighthill-Kuo (EPLK) method to obtain the Korteweg–de Vries (KdV) equations, which govern the nonlinear excitation of electrostatic solitons. Furthermore, the phase shift equations due to the collisions between electrostatic solitons are obtained. A theoretical analysis is improved by employing the KdV equations with the effects of the fifth – order dispersion terms. The numerical illustrations demonstrate that the higher-order soliton energy depends significantly on the quantum semiconductor plasma number density. On the other hand, the density of the semiconductor plasma has a weak effect on the lowest-order soliton energy. Therefore, one has to be careful about the choosing semiconductor plasma parameters to avoid any deficiency of the modern semiconductor devices.

In this work, we study, in a systematic way, dust-acoustic modulated envelope structures such as rogue waves (unstable waves) and dark soliton (stable waves) collisions in a complex plasma with nonthermal ions and Boltzmann electrons. In the present plasma system, we can have both negative and positive potential structures associated with the nonlinear dust-acoustic structures. Therefore, we derived the modified Korteweg–de Vries (mKdV) equation, by using the reductive perturbation technique, to describe the nonlinear structures at critical plasma parameters. For studying the properties of the modulated envelope structures, the mKdV equation transformed to a nonlinear Schrödinger equation. Depending on the modulational instability analysis, the stability and instability regions for the propagating nonlinear modulated waves have been determined precisely. After that, the properties of the dust-acoustic rogue waves are examined within the instability regions. Moreover, the effects of physical parameters, such as the ion-to-electron temperature ratio and the ion nonthermal parameter on the profile of dust-acoustic rogue waves are examined. Furthermore, our investigations extended to study the head-on collisions of two-dark solitons in the stability regions. Using the extended Poincaré–Lighthill–Kuo perturbation method, the dark solitons in the present plasma system develop according to two quasi-Korteweg–de Vries equations. After that, the phase shifts induced by the face-to-face collisions between two-dark solitons are obtained analytically. Also, the effects of the above physical parameters on the phase shifts are reported. The results may have relevance in space and laboratory dusty plasmas.

Freak wave is the common wave which has significant wave height and irregular wave shape, and it is easy to damage offshore structure extremely. The FPSOs (Floating Production Storage and Offloading) suffer from the environment loads, including the freak wave. The freak waves were generated based on the improved phase modulation model, and the coupling model of FPSO-SPM (Single Point Mooring) was established by considering internal-turret FPSO and its mooring system. The dynamic response characteristics of both FPSO and SPM affected by the freak wave were analyzed in the time domain. According to the results, the freak waves generated by original phase modulation model mainly affect the 2nd-order wave loads. However, the freak waves which are generated by random frequencies phase modulation model affect both 1st-order and 2nd-order wave loads on FPSO. What is more, compared with the irregular waves, the dynamic responses of mooring system are larger in the freak waves, but its amplitude lags behind the peak of the freak wave.

The probability of the existence of the ion-acoustic rogue waves in a plasma composed of warm ions and non-Maxwellian (nonthermal or Kappa) electrons is investigated in the framework of the modified Korteweg-de Vries (mKdV) equation. Using the reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. After numerical analysis, it is found that the present plasma system populated with nonthermal (Cairns) electrons leads to generation of compressive and rarefactive pulses, in contrast to the case of Kappa distribution. Thus, only for the nonthermal populated electrons, there is a critical value of the nonthermal parameter at which the coefficient of the nonlinear term of the KdV equation vanishes. In this case, we derived the modified KdV (mKdV) equation to describe the evolution of the system. To investigate the rogue waves propagation in our system, the mKdV equation should transfer to the nonlinear Schrödinger equation (NLSE). Our results provide a better understanding of observations in space plasmas which indicate the existence of nonthermal particles.

The majority electron density as a function of the Fermi energy is calculated in zinc blende, n-type GaSb for donor densities between 10 -16 cm-3 and 1019 cm-3. These calculations solve the charge neutrality equation self-consistently for a four-band model (three conduction sub-bands at Γ, L, and X and one equivalent valence band at Γ) of GaSb. Our calculations assume parabolic densities of states and thus do not treat the density-of-states modifications due to high concentrations of dopants, many body effects, and non-parabolicity of the bands. Even with these assumptions, the results are important for interpreting optical measurements such as Raman measurements that are proposed as a non-destructive method for wafer acceptance tests.

The generation of ion-acoustic rogue waves in ultracold neutral plasmas (UNPs) composed of ion fluids and nonextensive electron distribution is investigated. For this purpose, basic equations are reduced to a nonlinear Schrödinger equation (NLSE) using a reductive perturbation technique. The existence region for the rogue waves defined precisely in terms of the critical wavenumber threshold kc
. It is found that increasing the nonextensive parameter q would lead to a decrease of kc
until q approaches to its critical value qc
, then further increase of q beyond qc
enhances kc
; however, kc
shrinks with the increase of the ions effective temperature ratio σ∗. The dependence of the first- and second-order rational solutions profile on the UNP parameters is numerically examined. It is noticed that near to the critical nonextensive parameter qc
, the rogue wave amplitude becomes smaller, but it enhances whenever we stepped away from qc
. However, the enhancement of the temperature ratio σ∗ and the wavenumber k reduces the envelope rogue wave amplitudes.

The ion-acoustic rogue waves in ultracold neutral plasmas consisting of ion fluid and nonthermal electrons are reported. A reductive perturbation method is used to obtain a nonlinear Schrödinger equation for describing the system and the modulation instability of the ion-acoustic wave is analyzed. The critical wave number kc, which indicates where the modulational instability sets in, has been determined. Moreover, the possible region for the ion-acoustic rogue waves to exist is defined precisely. The effects of the nonthermal parameter β and the ions effective temperature ratio σ∗ on the critical wave number kc are studied. It is found that there are two critical wave numbers in our plasma system. For low wave number, increasing β would lead to cringe kc until β approaches to its critical value βc, then further increase of β beyond βc would enhance the values of kc. For large wave numbers, the increase of β would lead to a decrease of kc. However, increasing σ∗ would lead to the reduction of kc for all values of the wave number. The dependence of the rogue waves profile on the plasma parameters is numerically examined. It is found that the rogue wave amplitudes have complex behavior with increasing β. Furthermore, the enhancement of σ∗ and the carrier wave number k reduces the rogue wave amplitude. It is noticed that near to the critical wave number, the rogue wave amplitude becomes high, but it shrinks whenever we stepped away from kc. The implications of our results in laboratory ultracold neutral plasma experiments are briefly discussed.

Propagation of waves in nano-sized GaAs semiconductor induced by electron beam are investigated. A dispersion relation is derived by using quantum hydrodynamics equations including the electrons and holes quantum recoil effects, exchange-correlation potentials, and degenerate pressures. It is found that the propagating modes are instable and strongly depend on the electron beam parameters, as well as the quantum recoil effects and degenerate pressures. The instability region shrinks with the increase of the semiconductor number density. The instability arises because of the energetic electron beam produces electron-hole pairs, which do not keep in phase with the electrostatic potential arising from the pair plasma.

Super rogue waves with an amplitude of up to 5 times the background value are observed in a water-wave tank for the first time. Nonlinear focusing of the local wave amplitude occurs according to the higher-order breather solution of the nonlinear wave equation. The present result shows that rogue waves can also develop from very calm and apparently safe sea states. We expect the result to have a significant impact on studies of extreme ocean waves and to initiate related studies in other disciplines concerned with waves in nonlinear dispersive media, such as optics, plasma physics, and superfluidity.

The focusing nonlinear Schrödinger equation, which describes
generic nonlinear phenomena, including waves in the deep ocean and light
pulses in optical fibres, supports a whole hierarchy of recently
discovered rational solutions. We present recurrence relations for the
hierarchy, the pattern of zeros for each solution and a set of integral
relations which characterizes them.

The Peregrine soliton is a localized nonlinear structure predicted to exist over 25 years ago, but not so far experimentally observed in any physical system. It is of fundamental significance because it is localized in both time and space, and because it defines the limit of a wide class of solutions to the nonlinear Schrödinger equation (NLSE). Here, we use an analytic description of NLSE breather propagation to implement experiments in optical fibre generating femtosecond pulses with strong temporal and spatial localization, and near-ideal temporal Peregrine soliton characteristics. In showing that Peregrine soliton characteristics appear with initial conditions that do not correspond to the mathematical ideal, our results may impact widely on studies of hydrodynamic wave instabilities where the Peregrine soliton is considered a freak-wave prototype

We report properties of solitary acoustic pulses that propagate in electron-hole quantum semiconductor plasmas. We show that the dynamics of nonlinear acoustic pulses is governed by the Korteweg-de Vries equation, which includes contributions of the electron and hole quantum recoil effects, quantum statistical pressures of the plasma species, as well as exchange and correlation effects. Typical values for GaAs, GaSb, GaN, and InP semiconductors are used to estimate the speed and profiles of solitary acoustic pulses. The nonlinear solitary pulses depict intrinsic localization of electrostatic wave energies in semiconductor plasmas. (C) 2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.4736726]

The nonlinear propagation of ion solitary pulses in a warm collisionless electron–positron–ion plasma with ultrarelativistic degenerate electrons and positrons has been investigated. Arbitrary and small-(but finite-) amplitude ion solitary pulses are investigated by deriving the Korteweg–de Vries equation and an energy-balance-like expression involving a Sagdeev-like pseudopotential. The existence regions for ion solitary pulses have been precisely defined and numerically investigated. The ion solitary pulse profiles are also displayed. Applications to the interior of white dwarf stars and the corona of magnetars are discussed.

Properties of nonlinear electrostatic solitary waves in a plasma are analyzed by using the hydrodynamic model for electrons, positrons, and relativistic electron beam. For this purpose, the Kadomtsev–Petviashvili (KP) equation has been derived and its analytical solution is presented. It is found that the nonlinear solitary structures can propagate as slow and fast modes. The dependence of these modes on the plasma parameters is defined numerically. Furthermore, positive and negative electrostatic solitary structures can exist. In order to show that the characteristics of the solitary wave profile are influenced by the plasma parameters, the relevant numerical analysis of the KP equation is obtained. The electrostatic solitary 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. V C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3698984]

In outer space physics and astrophysics, there is a considerable amount of anomalous phenomena that support nonextensive particle distribution. This is because of the relevance of gravitational forces (which are long ranged) as well as to a variety of dynamical nonlinear aspects. Here, we investigate the nonlinear properties and the existence conditions of a plasma system consisting of ion fluid as well as electrons and positrons modelled by nonextensive distributions. The numerical analysis of the evolution equation shows that both subsonic and supersonic electrostatic waves may exist. These nonlinear waves admit positive and negative localized structures. The dependence of the latter on the plasma parameters is investigated numerically. V C 2012 American Institute of Physics. [doi:

Rogue wave in a collisionless, unmagnetized electronegative plasma is investigated. For this purpose, the basic set of fluid equations is reduced to the Korteweg-de Vries (KdV) equation. However, when the frequency of the carrier wave is much smaller than the ion plasma fre-quency then the KdV equation is also used to study the non-linear evolution of modulationally unstable modified ion-acoustic wavepackets through the derivation of the nonlinear Schrödinger (NLS) equation. In order to show that the char-acteristics of the rogue wave is influenced by the plasma pa-rameters, the relevant numerical analysis of the NLS equa-tion is presented. The relevance of our investigation to the Titan's atmosphere is discussed.

Generation of nonlinear ion-acoustic waves in a plasma having nonextensive electrons and positrons has been studied. Two wave modes existing in such plasma are considered, namely solitary and rogue waves. The reductive perturbation method is used to obtain a Korteweg-de Vries equation describing the system. The latter admits solitary wave pulses, while the dynamics of the modulationally unstable wave packets described by the Korteweg-de Vries equation gives rise to the formation of rogue excitation that is described by a nonlinear Schrödinger equation. The dependence of both solitary and rogue waves profiles on the nonextensive parameter, positron-to-ion concentration ratio, electron-to-positron temperature ratio, and ion-to-electron temperature ratio are investigated numerically. The results from this work are expected to contribute to the in-depth understanding of the nonlinear excitations that may appear in nonextensive astrophysical plasma environments, such as galactic clusters, interstellar medium, etc. V C 2011 American Institute of Physics. [doi:

Progress in understanding the nonlinear Langmuir rogue waves which accompany collisionless electron-positron e-p plasmas is presented. The nonlinearity of the system results from the nonlinear coupling between small, but finite, amplitude Langmuir waves and quasistationary density perturbations in an e-p plasma. The nonlinear Schrödinger equation is derived for the Langmuir waves' electric field envelope, accounting for small, but finite, amplitude quasistationary plasma slow motion describing the Langmuir waves' ponderomotive force. Numerical calculations reveal that the rogue structures strongly depend on the electron/positron density and temperature, as well as the group velocity of the envelope wave. The present study might be helpful to understand the excitation of nonlinear rogue pulses in astrophysical environments, such as in active galactic nuclei, in pulsar magnetospheres, in neutron stars, etc. © 2011 American Institute of Physics.

A general quantum dispersion equation for electron-positron(hole)-ion quantum plasmas is
derived and studied for some interesting cases. In an electron-positron-ion degenerate
Fermi gas, with or without the Madelung term, a new type of zero sound waves are found.
Whereas in an electron-hole-ion plasmas a new longitudinal quantum waves are revealed,
which have no analogies in quantum electron-ion plasmas. The excitation of these quantum
waves by a low-density monoenergetic straight electron beam is examined. Furthermore, the
Korteweg-de Vries (KdV) equation for novel quantum waves is derived and the contribution
of the Madelung term in the formation of the KdV solitons is discussed.

We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schrödinger equation. The critical wave-number threshold k(c), which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k(c) against the nonextensive parameter q are found. For small k(c), it is found that increasing q would lead to an increase of k(c) until q approaches a certain value q(c), then further increase of q beyond q(c) decreases the value of k(c). For large k(c), the critical wave-number threshold k(c) is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.

Freak waves are very large, rare events in a random ocean wave train. Here we study their generation in a random sea state characterized by the Joint North Sea Wave Project spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schrödinger (NLS) equation. We show from extensive numerical simulations of the NLS equation how freak waves in a random sea state are more likely to occur for large values of the Phillips parameter alpha and the enhancement coefficient gamma. Comparison with linear simulations is also reported.

The evolution of hole Peregrine soliton (appearing as a deep trough
between two crests) from ion-acoustic perturbations excited in a
multicomponent plasma with critical density of negative ions has been
observed. The observed soliton is described by the rational solution of
the cubic nonlinear Schrödinger equation, which can appear as an
isolated high peak or a deep hole depending on the phase of the
underlying carrier wave relative to the envelope. The measured amplitude
of the hole Peregrine soliton (depth from crest to trough) is found to
be more than twice the background wave height. The experimental
observations are compared with the theoretical results obtained from the
solution of the cubic nonlinear Schrödinger equation. The frequency
spectrum of the Peregrine soliton is analyzed and found to be triangular
in shape.

DOI:https://doi.org/10.1103/PhysRevLett.17.996

We predict the existence of rogue waves in Bose-Einstein condensates either loaded into a parabolic trap or embedded in an optical lattice. In the latter case, rogue waves can be observed in condensates with positive scattering length. They are immensely enhanced by the lattice. Local atomic density may increase up to tens times. We provide the initial conditions necessary for the experimental observation of the phenomenon. Numerical simulations illustrate the process of creation of rogue waves.

We have numerically calculated chaotic waves of the focusing nonlinear Schrr̈odinger equation (NLSE), starting with a plane wave modulated by relatively weak random waves. We show that the peaks with highest amplitude of the resulting wave composition (rogue waves) can be described in terms of exact solutions of the NLSE in the form of the collision of Akhmediev breathers.

The electron–hole two-stream instability in a quantum semiconductor plasma has been studied including
electrons and holes quantum recoil effects, exchange-correlation potentials, and degenerate pressures of
the plasma species. Typical values of GaAs and GaSb semiconductors are used to estimate the growth
rate of the two-stream instability. The effects of electron– and hole–phonon collision, quantum recoil
effects, the streaming velocities, and the corresponding threshold on the growth rate are investigated
numerically. Considering the phonon susceptibility allows the acoustic mode to exist and the collisional
instability arises in combination with drift of the holes.

We study the effect of various perturbations on the fundamental rational solution of the nonlinear Schrödinger equation (NLSE). This solution describes generic nonlinear wave phenomena in the deep ocean, including the notorious rogue waves. It also describes light pulses in optical fibres. We find that the solution can survive at least three types of perturbations that are often used in the physics of nonlinear waves. We show that the rational solution remains rational and localized in each direction, thus representing a modified rogue wave.

The experimental observation of Peregrine solitons in a multicomponent plasma with the critical concentration of negative ions is reported. A slowly amplitude modulated perturbation undergoes self-modulation and gives rise to a high amplitude localized pulse. The measured amplitude of the Peregrine soliton is 3 times the nearby carrier wave amplitude, which agrees with the theory. The numerical solution of the nonlinear Schrödinger equation is compared with the experimental results.

The effects of possible imperfections on the infrared optical absorption and on the charge-density profile of wide parabolic quantum wells (WPQW's) are studied. We consider effects that can arise from the finite width of WPQW's, from the existence of a quartic component in the confining potential, and from the existence of a region of flat potential in the center of the well. Within the local-density approximation, we confirm that a perfect WPQW absorbs light only at the bare harmonic-oscillator frequency, and show that the effects of small imperfections of the types considered on the absorption spectrum are twofold: a shift in the location of the main peak and the appearance of new peaks nearby.