We consider the formation of the periodic structures named dunes, which were observed during auroral events and were presented in the form of a set of almost horizontal stripes of green emission with an estimated period of 45 +/- 14 km at some altitude in the altitude range of 90-110 km. Most observations of this event refer to October, the time when the high-speed meteor shower Draconids occurs. During high-speed meteor showers ablation of meteors in the lower ionosphere and subsequent condensation of the evaporated substance results in the formation of a dusty ionospheric plasma (Kopnin S.I. et al., Phys. Plasmas 16 , 063705 (2009)). At the altitudes of about 100 km the modulational instability in dusty plasmas can develop leading to an appearance and growth of dust acoustic waves. If the growth is not compensated by other effects at early stage, the wave perturbations can become intensive enough to form a nonlinear periodic wave structure. We show that the formation of the dunes observed in the altitude range of 90-110 km during the period of Draconids meteor shower can be associated with such nonlinear periodic dust acoustic wave structures.

A characteristic feature of the magnetosphere of Saturn is the presence of two types of electrons, hot and cold ones, which obey kappa distributions. Electrons, magnetospheric ions, and dust particles, which have been discovered within the Cassini mission, form a dusty plasma system in the magnetosphere of Saturn. Nonlinear periodic dust acoustic waves of arbitrary amplitude, which can propagate in the dusty magnetosphere of Saturn, are considered. The obtained results are important for the interpretation of future space observations.

A mechanism of formation of plasma-dust system above the surface of Enceladus, the Saturn moon, illuminated by the solar radiation is proposed. It is demonstrated that the photoelectric effect caused by the sunlight and the influence of the solar-wind plasma create conditions for lifting of dust particles above the surface of the moon as a result of electrostatic repulsion. Based on a self-consistent model describing the electrostatic field and plasma components, including photoelectrons emitted from the Enceladus surface and those emitted from the surface of the dust particles, distribution functions of photoelectrons, dust particles, and their electrostatic charges are determined as functions of altitude and the angle between the local normal and the direction to the Sun. Also determined are the altitude profiles of the electrostatic fields for the corresponding angles between the local normal and the direction of the solar radiation. It is demonstrated that the photoelectric effect plays an important role in formation of dusty plasma near the Enceladus surface despite considerable distance from the Sun. It is established that concentration of photoelectrons above the Enceladus surface can exceed concentration of electrons and ions of the solar wind by an order of magnitude, and the size of the levitating particles is larger than the characteristic size of dust particles lifted above the surface of the Moon due to the fact that Enceladus is much smaller than the Moon. On the contrary, the size of particles levitating above Enceladus is much smaller than the size of particles levitating above the surface of celestial objects smaller than the Enceladus, e.g., the Martian satellites Phobos and Deimos.

A description is given of low-frequency nonlinear dust acoustic waves in Saturn’s dusty magnetosphere, which contains electrons of two types (hot and cold) obeying the kappa distribution, magnetospheric ions, and charged dust particles. For the corresponding conditions, the derivation of the Zakharov–Kuznetsov equation is given, which describes the nonlinear dynamics of dust acoustic waves in the case of low frequencies and a pancake-shaped wave packet along an external magnetic field. It is shown that under the conditions of Saturn’s magnetosphere there exist solutions of the Zakharov–Kuznetsov equation in the form of one-dimensional and three-dimensional solitons. Possible observations of the considered solitons in future space missions are discussed.

In the Earth’s atmosphere at altitudes of 80–120 km during high-speed meteor showers, conditions are created for the appearance of a dusty plasma system. As a result of the development of the modulation instability of the electromagnetic waves, in the dusty ionospheric plasma, linear and nonlinear dust acoustic waves can be excited. The new phenomenon observed above the Scandinavian countries, the so-called dunes, which are, in fact, periodic wave structures that extend to far distances in the horizontal direction and have a characteristic spatial period of about 45 km, can be one of the manifestations of the nonlinear dust acoustic waves. The maximum number of dunes was recorded in October, when the Draconids meteor shower is observed. We consider the nonlinear periodic dust acoustic waves that can develop in the dusty plasma with parameters that correspond to the ionospheric plasma during meteor showers.

Представлено двумерное описание нелинейных пылевых звуковых волн в запыленной магнитосфере Сатурна, которая содержит электроны двух сортов (горячие и холодные), подчиняющиеся каппа-распределению, ионы магнитосферы, а также заряженные пылевые частицы. Для условий запыленной магнитосферы Сатурна приведен вывод уравнения Кадомцева–Петвиашвили, описывающего нелинейную динамику почти одномерных волновых структур. Рассмотрена возможность распространения локализованных волновых структур типа пылевых звуковых солитонов. Показано, что в условиях магнитосферы Сатурна существуют решения уравнения Кадомцева–Петвиашвили в виде одномерных солитонов и двумерных N -солитонов. Обсуждаются возможные наблюдения рассматриваемых солитонов в будущих космических миссиях.

Two-dimensional description of nonlinear dust-acoustic waves in the dusty Saturn’s magnetiosphere that contains electrons of two types (the hot and the cold ones) obeying the kappa distribution, along with magnetospheric ions and charged dust particles, is presented. The Kadomtsev–Petviashvili equation that describes the nonlinear dynamics of the nearly one-dimensional wave structures is derived for the conditions of the dusty Saturn’s magnetosphere. The possibility of propagation of localized wave structures of the dust-acoustic soliton type is analyzed. It is demonstrated that the Kadomtsev–Petviashvili equation has solutions in the form of one-dimensional solitons and two-dimensional N -solitons under the conditions of the Saturn’s magnetosphere. The possibility of observation of the discussed solitons during future space missions is discussed.

Abstract—Modified Kadomtsev–Petviashvili equation describing nonlinear dynamics of nearly one-dimensional wave structures in dusty plasma above illuminated part of the Moon in the situation in which localization along magnetic-field vector is much stronger than along other directions is derived. The equation differs from the ordinary Kadomtsev–Petviashvili equation by the nonlinear term being non-analytical. Modified Kadomtsev–Petviashvili differs from generalizations of the Kadomtsev–Petviashvili equation in which nonlinearity retains the same form as in the ordinary Kadomtsev–Petviashvili equation but higher-order corrections for dispersion are taken into account. An analytical expression governing one-dimensional soliton solution to the modified Kadomtsev–Petviashvili equation is obtained. The solution differs from the well-known one-dimensional soliton solutions to the Korteweg–De Vries and ordinary Kadomtsev–Petviashvili equations. Stability analysis of the one-dimensional soliton solution showed that it is stable. Possible applications of the discussed solitons from the point of view of description of the so-called transient lunar phenomena representing short-lived light, changes in color or appearance on the surface of the Moon are discussed.

The possibility is considered of propagation of localized wave structures, such as dust acoustic solitons, in the plasma of the dust-filled Saturn’s magnetosphere, which contains electrons of two sorts (hot and cold) subject to kappa distribution, ions, and charged dust grains. The ranges of possible velocities and amplitudes of the solitons are determined. Soliton solutions for different sizes and concentrations of dust grains in the dust-filled Saturn’s magnetosphere are found.

The nonlinear equation is obtained describing the dynamics of nonlinear wave structures in the dusty plasma above the illuminated surface of the Moon in the case of low frequencies and pancake-like shape of wave packet in the direction along the external magnetic field. This equation is the modified Zakharov – Kuznetsov equation. The analytical formula for the one-dimensional soliton solution is derived. The analysis of the stability of one-dimensional soliton solution was performed.

This paper shows a possibility of the existence and propagation of dust acoustic solitons in plasmas of dusty exosphere of the Moon, which contains, in addition to electrons and ions of the solar wind and photoelectrons from the lunar surface, also charged dust particles, as well as photoelectrons emitted from the surfaces of these particles. Soliton solutions are found and the ranges of possible velocities and amplitudes of such solitons are determined depending on the height above the lunar surface for different subsolar angles.

We demonstrate the possibility of the existence and propagation of dust acoustic solitons in the dusty plasma of the lunar exosphere, which contains, in addition to electrons and ions of the solar wind and photoelectrons from its surface, charged dust particles, as well as photoelectrons emitting from the surfaces of these particles. Soliton solutions are found and the ranges of possible velocities and amplitudes of such solitons are determined depending on the height above the lunar surface for different subsolar angles.

The possible propagation of localized wave structures such as dust-acoustic solitons in dusty ionospheric plasma containing photoelectrons, electrons and ions of the ionosphere, and charged dust particles is considered. Intervals of the possible soliton velocities and amplitudes are determined. Solitary wave solutions for various dimensions and concentrations of particles in dusty ionospheric plasma are found.

A possibility of propagation of localized wave structures, such as dust acoustic solitons, in dusty ionospheric plasmas, which contain photoelectrons, electrons and ions, as well as charged dust particles, is considered. The regions of possible velocities and amplitudes of solitons are determined. Soliton solutions are found for various sizes and number densities of dust particles in the dusty ionospheric plasmas.

The effect of hydrogen-containing compounds in the regolith on the properties of dusty plasma near the surface of the Moon is investigated. The calculation of the size distributions and heights of the rise of charged dust particles over the illuminated parts of the surface of the Moon enriched with hydrogen has been performed. It has been demonstrated that dust particles floating above hydrogen-rich sites have larger sizes and larger charges, and also reach higher altitudes than in a situation when dust hovers over areas of lunar regolith not enriched with hydrogen. The possibility of the release from the crystal lattice of silicon dioxide in the lunar regolith of oxygen atoms as parts of silver hydroxide molecules is shown. Silver hydroxide, in turn, can relatively easily react with hydrogen, which leads to the formation of water and silver. This shows the possibility of the formation of water molecules included in the near-surface lunar soil. The presence of water molecules in the lunar soil can also affect the photoelectric properties of the lunar regolith and the parameters of the plasma-dust system over the Moon.

Linear and nonlinear waves in the near-surface plasma at Phobos and Deimos are considered. It is shown that the motion of the solar wind relative to photoelectrons and charged dust grains violates the isotropy of the electron distribution function in the near-surface plasma at the Martian satellites, which leads to the development of instability and excitation of high-frequency waves with frequencies in the range of Langmuir and electromagnetic waves. Moreover, the propagation of dust acoustic waves, which can be excited, e.g., in the terminator regions of the Martian satellites, is possible. Solutions corresponding to the parameters of the plasma–dust systems over the illuminated parts of the Phobos and Deimos surfaces are found in the form of dust acoustic solitons. The ranges of possible Mach numbers and soliton amplitudes are determined.