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Nonlinear electrostatic waves on the ion time scale have been studied in a quantum magnetoplasma in the presence of relativistically degenerate electrons. In this regard, Zakharov Kuznetsov (ZK) equation has been derived using the reductive perturbation technique. The single and two soliton solutions of the ZK equation have been obtained by employing Hirota formalism. The nonrelativistic and ultrarelativistic limits of the relativistically degenerate electrons have been studied and discussed in detail for important plasma parameters both for the single and two soliton solutions of the ZK equation. We have applied our study for the plasma parameters that are found in the white dwarfs. It has been noticed that the interaction of the ZK solitons depends on the propagation vectors in the predominant direction of propagation. Importantly, it has been found that the spatial and temporal scales over which the interaction of solitons occur are different for the nonrelativistic and ultrarelativistic cases. [ABSTRACT FROM AUTHOR]

The progression of nonlinear electron-acoustic waves (EAWs) in a magnetized and collision-free plasma made up of cold inertial electrons, inertialess superthermal electrons, and stationary background ions with special reference to Saturn's magnetosphere (SMS) is explored. The method of reductive perturbation (MRP) is employed to obtain the evolution equation (i.e., Zakharov– Kuznetsov equation (ZKE)) that governs the propagation of electron acoustic solitons (EASs). Using the elegant and efficient Hirota bilinear method (HBM), multi-soliton solutions (MSSs) of the ZKE are determined. The impact of the effects of hot-to-cold electron density ratio, magnetic field (MF) strength, and superthermality on single as well as the interaction of EASs is examined. Estimates of the values of the electric field at several radii of SMS (i.e., 12 R s − 17.8 R s , where R s is the radius of Saturn) are presented, which are found in μV / m to mV / m range and are in perfect agreement with the data from Cassini radio and plasma wave science wideband receiver. Moreover, the influence of the relevant plasma parameters on the interaction time and spatial extent of the interacting EASs is also explored. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the electrostatic electron Bernstein waves in a collisionless magnetized plasma using the Cairns distribution function. In this regard, we have derived a generalized dielectric constant for the Bernstein waves and derived the modified dispersion relation in the presence of Cairns distribution function. We have found that the dispersion curves for the electron Bernstein waves using the Cairns distribution function show a very significant deviation from the Maxwellian results. It has been found that the behavior of the Bernstein waves across the entire band between the adjacent harmonics shows a departure from the Maxwellian result for the different values of the non-thermality parameter for the Cairns distribution function. Key words: electron Bernstein waves, collisionless magnetoplasma, Cairns distribution function, electrostatic electrons, nonthermal parameter. Nous utilisons la fonction de distribution de Cairns pour etudier les ondes electroniques electrostatiques de Bernstein dans un plasma magnetise sans collision. A cette fin, nous derivons une expression generalisee de la constance dielectrique pour les ondes de Bernstein et obtenons la relation de dispersion modifiee dans le cadre de la fonction de distribution de Cairns. Nous trouvons que les courbes de dispersion des ondes electroniques de Bernstein en utilisant la distribution de Cairns devient tres significativement des resultats utilisant la distribution de Maxwell. Nous trouvons que le comportement des ondes de Bernstein sur l'ensemble de la bande entre les harmoniques adjacents se differencie des valeurs de Maxwell pour les differentes valeurs du parametre de non-thermalite de la fonction de distribution de Cairns. [Traduit par la Redaction] Mots-cles : ondes electroniques de Bernstein, magneto-plasma sans collision, fonction de distribution de Cairns., 1. Introduction Satellite missions in astrophysical and space plasmas have regularly observed particle distribution functions that are quasi-Maxwellian up to the mean thermal velocities and possess non-Maxwellian suprathermal tails at [...]

The presence of the geometrical curvature makes the planar Korteweg–de Vries (KdV) equation inadequate to describe the propagation of nonlinear waves. In many scientific disciplines including plasma physics, nonlinear optics, oceanography, and communications, the cylindrical KdV (CKdV) equation becomes the appropriate choice for modeling these waves. Motivated by these applications, the Bäcklund transformation is used to analyze and find an analytical solution to the CKdV equation in the present investigation. For the first time, the multi-soliton solutions, including single-, two-, and three-soliton solutions, are investigated, and a general scheme is given to find N-soliton solutions of the CKdV equation in the context of plasma physics. Numerous researchers may find the given solutions helpful in understanding the mechanism of the generation of multi-solitons in their laboratory experiments and may also engender interest in the space physics community to look for these structures in the data coming from a variety of satellites roaming in space. [ABSTRACT FROM AUTHOR]

In view of the recent observations by plasma science-spacecraft-voyager and Cassini plasma spectrometer of Saturn's magnetosphere, the interaction between two counter-propagating ion-acoustic (IA) solitons is studied in an unmagnetized plasma consisting of warm adiabatic ions in addition to hot and cold electrons following kappa distribution. The head-on collision of the IA solitons is investigated using the extended Poincare–Lighthill–Kuo technique. Since this model supports both compressive and rarefactive solitons, therefore, the soliton collisions for both Korteweg–de Vries (KdV) and the modified KdV (mKdV) equations are investigated. The corresponding phase shifts after the collision for both these equations are also derived and examined. Furthermore, the effects of different plasma parameters (corresponding to Saturn's magnetosphere), including superthermality, density, and temperature on the colliding soliton profiles and their phase shifts, are examined. It is concluded that the phase shift is smaller when both hot and cold electrons are Maxwellian by comparison with the superthermal case. [ABSTRACT FROM AUTHOR]

The purpose of this study is to examine the properties of the dust-acoustic solitary waves in a complex magnetoplasma made up of negatively charged moving dust grains in the lower ionospheric region and inertialess electrons and ions obeying Maxwell and kappa distributions, respectively. In this context, the reductive perturbation technique is carried out to obtain the Zakharov–Kuznetsov (ZK) equation within the given framework. The obtained evolution equation, i.e., ZK equation is transformed to a planar dynamical system for studying the qualitative behavior of the solitary waves. The impact of important physical parameters, such as the dust number density, ion concentration, ion temperature, superthermality, and the background magnetic field, on the profile of the nonlinear structures is numerically investigated. The findings may be utilized to comprehend the low-frequency irregularities that are detected in the lower ionosphere. [ABSTRACT FROM AUTHOR]