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Динамика бризера на глубокой воде под действием ветра
Гл. 10. С. 46–48.
Abrashkin A. A., Oshmarina O. E.
Publication based on the results of:
In book
Каз.: Издательство Казанcкого государственного университета, 2015.
Abrashkin A. A., Journal of Mathematical Fluid Mechanics 2025 Vol. 27 Article 59
Three-dimensional hydrodynamic equations of ideal incompressible fluid in Lagrangian form are considered. Their explicit solution is obtained. The trajectories of fluid particles are complex spatial curves depending on four frequencies. The vortex lines precess around the vertical axis. Their shape is determined by an arbitrary function depending on the axial Lagrangian coordinate. It is shown ...
Added: October 23, 2025
A. A. Abrashkin, E. N. Pelinovsky, Radiophysics and Quantum Electronics 2023 Vol. 66 No. 2-3 P. 116–128
By convention, water waves are studied under the assumption of their potentiality. This approx imation is not always valid in natural conditions. The vorticity is introduced by shear currents, which are ubiquitous in the ocean. It is also generated in the near-surface layer as a result of wind action. When these factors are taken into ...
Added: January 21, 2025
Abrashkin A. A., Pelinovsky E., Известия высших учебных заведений. Радиофизика 2023 Т. LXVI № 2-3 С. 130–144
By tradition, water waves are studied under the assumption of their potentiality. The vorticity is introduced by shear currents which are ubiquitous in the ocean. It is also generated in near-surface layer as a result of wind action. When these factors are taken into account, the models developed for pitential waves require refinement and generalization. ...
Added: September 12, 2023
Pelinovsky E., Abrashkin A. A., Theoretical and Mathematical Physics 2023 Vol. 215 No. 2 P. 599–608
We review exact solutions for gravity waves in deep water. All of them are obtained within the Lagrangian framework and are generalizations of Gerstner waves (to the cases of inhomogeneous pressure on the free surface and taking the rotation of the fluid into account). The Cauchy invariants are found for each type of waves. ...
Added: June 25, 2023
Abrashkin A. A., E.Н. Пелиновский, Теоретическая и математическая физика 2023 Т. 215 № 2 С. 165–175
A review of exact solutions for gravitational waves in deep water is given. All of them are obtained within the framework of the Lagrangian description and are generalizations of Gerstner waves (for cases of inhomogeneous pressure on the free surface and taking into account the rotation of the fluid). The Cauchy invariants are found for ...
Added: June 25, 2023
Kachulin D., Dyachenko A., Gelash A., Fluids 2019 Vol. 4 No. 2 Article 83
We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water—breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow ...
Added: October 22, 2022
Kachulin D., Dremov S., Dyachenko A., Fluids 2021 Vol. 6 No. 3 Article 115
This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations ...
Added: October 22, 2022
Kachulin D., Dyachenko A., Dremov S., Fluids 2020 Vol. 5 No. 2 Article 65
The paper presents the long-time dynamics with multiple collisions of breathers in the super compact Zakharov equation for unidirectional deep water waves. Solutions in the form of breathers were found numerically by the Petviashvili method. In the terms of envelope and the assumption of the narrow spectral width the super compact equation turns into the ...
Added: October 22, 2022
Abrashkin A. A., Pelinovsky E., Physics-Uspekhi 2022 Vol. 65 P. 453–467
To mark 220 years since the appearance of Gerstner's paper that proposed an exact solution to the hydrodynamic
equations, an overview of exact solutions for water waves is given, each of which is a generalization of the Gerstner wave. Additional factors are coastal geometry, fluid rotation, varying pressure on the free surface, stratification, fluid compressibility, and background flows. Waves on ...
Added: October 13, 2022
Didenkulova E., Physica D: Nonlinear Phenomena 2022 Vol. 432 Article 133130
Breathers or oscillating wave packets, along with solitons, are the most energy-carrying waves in various physical media, i.e. surface and internal waves, optical networks, and Josephson junctions. Breathers largely determine the overall wave dynamics of wave fields. In this work, the dynamics of a set of breathers or the so-called breather turbulence or breather gas ...
Added: January 26, 2022
Mosharev P., Кечкин О. В., Moscow University Physics Bulletin 2020 Vol. 75 No. 5 P. 427–433
An exact expression is obtained for harmonic fields in Maxwell electrodynamics with dilatons in terms of elliptic Jacobi functions and elliptic Legendre integrals. The case of centrally symmetric fields is considered individually and effective charges of all three types, that is, electric, magnetic, and dilaton charges, are calculated. An expression is given for the generalized ...
Added: September 28, 2021
Кечкин О. В., Mosharev P., Moscow University Physics Bulletin 2020 Vol. 75 No. 3 P. 192–197
The effective Lagrangian is derived and a group of hidden symmetries is determined for Maxwell’s theory with an axion in the stationary case. The general harmonic solution is constructed, and it is shown that a central source can have only a Coulomb-type magnetic field. The electric field of such a source has a complex potential, ...
Added: September 16, 2021
L I Kuzmina, Osipov Y. V., , in: IOP Conference Series: Materials Science and EngineeringVol. 913: International Scientific Conference "Construction and Architecture: Theory and Practice of Innovative Development" (CATPID-2020) - Part 1 26-30 September 2020, Nalchik, Russian Federation.: IOP Publishing, 2020. Ch. 032066 P. 1–8.
Chemical reactions in a porous medium are found in many natural phenomena and
technological processes. Reactive substances dissolved in groundwater can significantly
change the soil strength. The precipitate formed as a result of the reaction changes the porous
medium structure and affects the porosity and permeability. A one-dimensional model of the
reaction of two reagents in a homogeneous porous ...
Added: January 7, 2021
Didenkulova E., Pelinovsky E., Fluids 2020 Vol. 5 P. 205
Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity
waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay
of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave
fields. In the present study, a series of numerical experiments on ...
Added: November 10, 2020
Didenkulova E., Pelinovsky E., Symmetry 2020 Vol. 12 No. 9 P. 1445
Pairwise interactions of particle-like waves (such as solitons and breathers) are important elementary processes that play a key role in the formation of the rarefied soliton gas statistics. Such waves appear in different physical systems such as deep water, shallow water waves, internal waves in the stratified ocean, and optical fibers. We study the features ...
Added: September 11, 2020
Sinelshchikov D., Garashchuk I., Kudryashov N. A., Journal of Physics: Conference Series 2017 Vol. 788 P. 012013 -1–012013 -6
Non-linear dynamical systems describe many physical processes. In this work we investigate a three-dimensional Lorenz-like system - the Glukhovsky-Dolzhansky system. We consider analytical properties of the studied system. The problem of existence of meromorphic solution is discussed. We perform the Painlev`e test and find conditions imposed on parameters of the system for which meromorphic solutions ...
Added: December 16, 2019
Sinelshchikov D., Garashchuk I., Kudryashov N. A., European Journal of Physics: Web of Conference 2018 Vol. 173 P. 03008-1–03008-4
We consider a generalization of the Rayleigh equation for the description of
the dynamics of a spherical gas bubble oscillating near an elastic or rigid wall. We show
that in the non–dissipative case, i.e. neglecting the liquid viscosity and compressibility, it
is possible to construct the general analytical solution of this equation. The corresponding
general solution is expressed via ...
Added: December 16, 2019
Rabinowitch A. S., Applied Mathematics 2010 Vol. 1 P. 1–7
Added: October 5, 2019