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## Formation of dispersive shock waves in evolution of a two-temperature collisionless plasma

Physics of Fluids. 2020. Vol. 32. Article 126115.

Ivanov S., Kamchatnov Anatoly M.

The nonlinear dynamics of pulses in a two-temperature collisionless plasma with the formation of dispersion shock waves is studied. An analytical description is given for an arbitrary form of an initial disturbance with a smooth enough density profile on a uniform density background. For large time after the wave breaking moment, dispersive shock waves are formed. Motion of their edges is studied in the framework of Gurevich–Pitaevskii theory and Whitham theory of modulations. The analytical results are compared with the numerical solution.

Ivanov S. K., Kamchatnov A.M., Physics of Fluids 2019 Vol. 31 Article 057102

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated, and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage ...

Added: February 4, 2021

Kamchatnov A.M., Chaos 2020 Vol. 30 Article 123148

The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the background flow, which interacts with the edge wave packets or the edge solitons. A conjecture about the existence ...

Added: February 4, 2021

Slunyaev A., Кокорина А. В., Journal of Ocean Engineering and Marine Energy 2017 Vol. 3 P. 395-408

The results of the probabilistic analysis of the direct numerical simulations of irregular unidirectional deep
water waves are discussed. It is shown that an occurrence of large-amplitude soliton-like groups represents an extraordinary case, which is able to increase noticeably the probability of high waves even in moderately rough sea conditions. The ensemble of wave realizations should be large enough to take these ...

Added: March 1, 2019

Kamchatnov A.M., Chaos 2019 Vol. 29 Article 023106

We discuss the problem of breaking of a nonlinear wave in the process of its propagation into a medium at rest. It is supposed that the profile of the wave is described at the breaking moment by the function (−x) 1/n (x < 0, positive pulse) or −x 1/n (x > 0, negative pulse) of ...

Added: February 4, 2021

Slunyaev A., Известия высших учебных заведений. Радиофизика 2018 Т. 61 № 1 С. 1-23

We propose a method for the analysis of groups of unidirectional waves on the surface of deep water, which is based on spectral data of the scattering problem in the approximation of a nonlinear Schrodinger equation. The main attention is paid to the robustness and accuracy of the numerically obtained spectral data. Various methods of choosing the wave ...

Added: March 1, 2019

Pelinovsky E., Dutykh D., Physical Letters A 2014 Vol. 378 No. 42 P. 3102-3110

The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV–BBM type models. Some high resolution numerical results are presented in both ...

Added: November 19, 2014

Диденкулова (Шургалина) Е. Г., Кокорина А. В., Slunyaev A., Вычислительные технологии 2019 Т. 24 № 2 С. 52-66

The details of the numerical scheme and the method of specifying the initial conditions for the simulation of the irregular dynamics of soliton ensembles within the framework of equations of the Korteweg – de Vries type are given using the example of the modified Korteweg – de Vries equation with a focusing type of nonlinearity. ...

Added: April 17, 2019

Ruderman M. S., Petrukhin N., Pelinovsky E., Solar Physics 2021 Vol. 296 Article 124

In this article we study the plasma motion in the transitional layer of a coronal loop randomly
driven at one of its footpoints in the thin-tube and thin-boundary-layer (TTTB) approximation. We introduce the average of the square of a random function with respect to time. This
average can be considered as the square of the oscillation amplitude ...

Added: August 18, 2021

Pelinovsky E., Touboil J., European J Mechanics B Fluids (Elsivier) 2014 Vol. 48 P. 13-18

The bottom pressure distribution under solitonic waves, travelling or fully reflected at a wall is analysed here. Results given by two kind of numerical models are compared. One of the models is based on the Green–Naghdi equations, while the other one is based on the fully nonlinear potential equations. The two models differ through the ...

Added: November 19, 2014

Slunyaev A., Studies in Applied Mathematics 2019 Vol. 142 P. 385-413

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation (GE) with positive cubic nonlinearity, which in the limits of small and large
amplitudes tends to other long-wave models, the classic and the modified Korteweg–de Vries equations. The local
solution for an isolated soliton or breather within the GE is obtained. ...

Added: March 11, 2019

Kamchatnov A.M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 99 No. 1 Article 012203

We suggest a method for calculation of parameters of dispersive shock waves in the framework of Whitham modulation theory applied to nonintegrable wave equations with a wide class of initial conditions corresponding to propagation of a pulse into a medium at rest. The method is based on universal applicability of Whitham’s “number of waves conservation ...

Added: February 4, 2021

Александров Н. Л., Ponomarev A., Физика плазмы 2018 Т. 44 № 10 С. 839-848

The process of relaxation of energetic O– ions formed via dissociative attachment of electrons to molecules in the discharge plasmas of water vapor and H2O: O2 mixtures in a strong electric field is studied by the Monte Carlo method. The probability of energetic ions being involved in threshold ion–molecular processes is calculated. It is shown ...

Added: November 20, 2019

Bondarenko G.G., Udris Y. Y., Fusion Engineering and Design 1998 Vol. 39-40 P. 419-426

The sputtering of a number of materials due to an intense polyenergetic flux of hydrogen particles has been investigated. The irradiation of pure tungsten, copper, aluminium, titanium, aluminium-lithium alloys, stainless steel and tungsten-copper composition has been carried out at particle flux densities of 1017-1018 cm~2 s~' and at fluences of 1020-1022 cm~2. Furthermore, W-Cu composition ...

Added: November 15, 2013

Peter Bespalov, Kuleshova V., Savilov A., Symmetry 2023 Vol. 15 No. 4 Article 838

In this study, kinetic interaction at the Cherenkov resonance between an electromagnetic wave pulse and a flow of electrons possessing a wide velocity spread at the scale of the characteristic range of the resonant electron wave interaction is considered. Due to the absence of a distribution function slope in the range of velocities corresponding to ...

Added: June 5, 2023

L. F. Calazans de Brito, A. M. Kamchatnov, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 109 No. 1 Article 015102

We consider nonlinear wave structures described by the modified Korteweg–de Vries equation, taking into account a small Burgers viscosity for the case of steplike initial conditions. The Whitham modulation equations are derived, which include the small viscosity as a perturbation. It is shown that for a long enough time of evolution, this small perturbation leads to the ...

Added: February 1, 2024

Boiti M., Pempinelli F., Pogrebkov A., Journal of Mathematical Physics 2011 Vol. 52 No. 083506 P. 1-21

Properties of Jost and dual Jost solutions of the heat equation, F (x,k)
and Y(x,k), in the case of a pure solitonic potential are studied in
detail.We describe their analytical properties on the spectral parameter k
and their asymptotic behavior on the x-plane and we show that the values
of e(−qx)F (x, k) and the residues of exp(qx ...

Added: February 16, 2013

S. S. Gavrilov, Physical Review B: Condensed Matter and Materials Physics 2020 Vol. 102 Article 104307

It is generally accepted that quantized vortices formed in coherent bosonic fluids are “excitations” and as such do not arise in a one-mode condensate at zero temperature. To excite them, one needs either inhomogeneities (impurities, rotation, etc.) or essentially finite fluctuations. Here, we predict a perfectly spontaneous formation of vortices even at zero temperature, which ...

Added: March 11, 2021

Bondarenko G.G., Kristya V. I., Savichkin D. O., Vacuum 2018 Vol. 149 P. 114-117

A model of field electron emission from the metal cathode with a thin insulating film under the strong
electric field, generated in the film by ions bombarding its surface in gas discharge, is developed. It takes
into account tunneling of electrons from the electrode metal substrate into the insulating film, their
motion in the film and going out ...

Added: March 12, 2018

O.E. Kurkina, A.A. Kurkin, T. Soomere et al., Physics of Fluids 2011 Vol. 23 No. 11 P. 116602-1-13-116602-13

We address a specific but possible situation in natural water bodies when the three-layer stratification has a symmetric nature, with equal depths of the uppermost and the lowermost layers. In such case, the coefficients at the leading nonlinear terms of the modified Korteweg-de Vries (mKdV) equation vanish simultaneously. It is shown that in such cases ...

Added: November 6, 2012

Borovitskaya I. V., Demin A. S., Komolova O. A. et al., Russian Metallurgy (Metally) 2023 Vol. 2023 No. 7 P. 891-898

The influence of pulsed helium ion (HI) and helium plasma (HP) fluxes on an Inconel 718 alloy
fabricated by an additive technology via selective laser melting and subsequent heat treatment is studied. The
structural changes in the surface layer (SL) after irradiation are analyzed for two different modes: soft (at radiation
power density q = 2 × 108 ...

Added: November 14, 2023

Ruderman M. S., Petrukhin N., Solar Physics 2022 Vol. 297 No. 6 Article 72

In this article we study the effect of a transitional layer in a magnetic tube on the real part
of the frequencies of kink oscillations. In our analysis, we use the model of a straight magnetic tube with the density and cross-section radius varying along the loop, and the thin-tube
thin-boundary (TTTB) approximation. First, we calculate the ...

Added: July 11, 2022

Ruderman M.., Petrukhin N., Astronomy and Astrophysics 2017 Vol. 600 No. A122 P. 1-11

The ability of phase mixing to provide eﬃcient damping of Alfvén waves even in weakly dissipative plasmas made it a popular mechanismforexplainingthesolarcoronalheating.Initiallyitwasstudiedintheequilibriumconﬁgurationswiththestraightmagnetic ﬁeldlinesandtheAlfvénspeedonlyvaryinginthedirectionperpendiculartothemagneticﬁeld.LatertheanalysisoftheAlfvénwave phase mixing was extended in various directions. In particular it was studied in two-dimensional planar magnetic plasma equilibria. Analytical investigation was carried out under the assumption that the wavelength is much smaller ...

Added: May 10, 2017

Копнин С.И., Морозова Т. И., Попель С.И., Физика плазмы 2019 Т. 45 № 9 С. 831-838

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 ...

Added: September 22, 2019

Bondarenko G.G., Udris Y. Y., Yakushin V. L., Fusion Engineering and Design 2000 Vol. 51-52 P. 81-84

The behaviour and erosion of tungsten, copper and W-Cu composition under irradiation by high intensive hydrogen plasma have been investigated. The erosion coefficients of these materials have been determined. The importance of copper redepositions in the mechanism of sputtering and erosion of W-Cu composition has been emphasised. ...

Added: November 21, 2013