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Волны Герстнера и их обобщения в гидродинамике и геофизике
Успехи физических наук. 2022. Т. 192. № 5. С. 491-506.
Abrashkin A. A., Pelinovsky E.
Publication based on the results of:
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
Abrashkin A. A., Chaos, Solitons and Fractals 2019 Vol. 118 P. 152-158
We present an analytical description of the class of unsteady vortex surface waves generated by non- uniformly distributed, time-harmonic pressure. The fluid motion is described by an exact solution of the equations of hydrodynamics generalizing the Gerstner solution. The trajectories of the fluid particles are circumferences. The particles on a free surface rotate around circumferences ...
Added: December 17, 2018
Abrashkin A. A., Discrete and Continuous Dynamical Systems 2019 Vol. 39 No. 8 P. 4443-4453
A class of non-stationary surface gravity waves propagating in the
zonal direction in the equatorial region is described in the f -plane approx
imation. These waves are described by exact solutions of the equations of
hydrodynamics in Lagrangian formulation and are generalizations of Gerstner
waves. The wave shape and non-uniform pressure distribution on a free sur
face depend on two ...
Added: June 19, 2019
Abrashkin A. A., Pelinovsky E., Izvestia, Atmospheric and Oceanic Physic 2018 Vol. 54 No. 1 P. 101-105
A nonlinear Schrцdinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously
vortical infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function
of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is
shown that the modulational instability criteria for the weakly vortical waves and ...
Added: October 3, 2018
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
Abrashkin A. A., Pelinovsky E., Physics-Uspekhi 2018 Vol. 61 P. 307-312
We discuss the properties of two-dimensional, non
linear, potential, and vortex waves on the surface of an ideal
liquid of infinite depth. It is shown that in the quadratic order in
the amplitude, the vorticity of the Gerstner wave is equal in
magnitude to and different in sign from that of the Stokes drift
current in a surface layer. This ...
Added: October 3, 2018
Abrashkin A. A., Deep-Sea Research Part II: Topical Studies in Oceanography 2019 Vol. 160 P. 3-6
Three Lagrangian invariants are shown to exist for flows in the equatorial region in the β - plane approximation.
They extend the Cauchy invariants to a non-rotating fluid. The relationship between these generalized invariants
and the results following from Kelvin's and Ertel's theorems is ascertained. Explicit expressions of the invariants
for equatorially trapped waves and equatorial Gerstner waves ...
Added: April 2, 2019
Aseeva N., Gromov E., Onosova I. V. et al., JETP Letters 2016 Vol. 103 No. 10 P. 653-657
Evolution of solitons is addressed in the framework of a third-order nonlinear Schrödinger equation (NLSE), including nonlinear dispersion, third-order dispersion and a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is well known as a part of the temporal domain NLSE in optics. In this context, it is induced by the ...
Added: June 28, 2016
Kurkina O. E., Kurkin A. A., Rouvinskaya E. et al., Письма в Журнал экспериментальной и теоретической физики 2012 Т. 95 № 2 С. 98-103
Nonlinear wave dynamics is discussed using the extended modified Korteweg–de Vries equation that includes the combination of the third- and fifth- order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are ...
Added: August 24, 2012
A. V. Slunyaev, T. V. Tarasova, Chaos 2022 Vol. 32 Article 101102
Synchronous collisions between a large number of solitons are considered in the context of a statistical description. It is shown that, during the interaction of solitons of the same signs, the wave field is effectively smoothed out. When the number of solitons increases and the sequence of their amplitudes decay slower, the focused wave becomes even smoother ...
Added: October 14, 2022
Musaev E., Akhmedov E., Gahramanov I., JETP Letters 2011 Vol. 93 No. 9 P. 545-550
The Polchinski equations for the Wilsonian renormalization group in the D-dimensional matrix scalar field theory can be written at large N in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) and can be found exactly for the subsector of Trϕ n (for all n) operators. We show that at ...
Added: October 20, 2014
Budkov Y., Journal of Physics: Condensed Matter 2019 Vol. 31 P. 078002-078003
We reply to the comment on our paper by Budkov (2018 J. Phys.: Condens. Matter 30 344001). ...
Added: January 4, 2019
CRC Press, 2016
In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors ...
Added: October 26, 2021
Elena R. Loubenets, Khrennikov A., Journal of Physics A: Mathematical and Theoretical 2019 Vol. 52 No. 43 P. 435304-1-435304-14
For an even qudit dimension d≥2, we introduce a class of two-qudit states exhibiting perfect correlations/ anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value 3/2 -- the upper bound attained on some ...
Added: September 26, 2019
Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416-432
We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...
Added: November 19, 2014
Dmitriev A., Kornilov V., Dmitriev V. et al., Frontiers in Physics 2022 Vol. 10 No. 839383 Article 839383
The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale water flows in the oceans. The detection ...
Added: March 14, 2022
Elena R. Loubenets, Kuznetsov S., Louis Hanotel, Journal of Physics A: Mathematical and Theoretical 2024 Vol. 57 No. 5 Article 055302
For the maximal violation of all Bell inequalities by an arbitrary pure two-qudit state of any dimension, we derive a new lower bound expressed via the concurrence of this pure state. This new lower bound and the upper bound on the maximal Bell violation, found in [J. Phys. A: Math. Theor. 55, 285301 (2022)] and ...
Added: January 6, 2024
Budkov Y., Kolesnikov A. L., Polymer Science - Series C 2018 Vol. 60 No. Supplement 1 P. 148-159
Theoretical models of the conformational behavior of flexible polymer chains in mixed solvents enunciated in the world literature during the last decade are critically reviewed. Models describing different mechanisms of coil-to-globule transitions in a good solvent induced by cosolvent addition are highlighted. Special attention is given to the analysis of theoretical approaches to describing the ...
Added: November 30, 2018
49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 2 P. 168-173
The parameters of unstable short-living isotopes are studied from
the mathematical point of view. The values of the chemical potential
and activity parameters that determine the neutron halo arising when
the neutron separates from the nucleus of an unstable isotope are
calculated. The analogy between nuclear physics and economics is
considered from the point of view of such parameters as ...
Added: August 25, 2019
Vostrikov A. V., Borisov N., Abrameshin A. E., Качество. Инновации. Образование 2013 № 8 (99) С. 61-65
In work research of numerical stability of earlier reduced scheme of numerical integration of system of the linear ordinary differential equations developed by authors is conducted. The received condition of numerical stability of the reducing scheme proves possibility of use of this scheme in practice. Operability of the reduced scheme was tested on a real ...
Added: September 9, 2013
Elena R. Loubenets, / Cornell University. Series arXiv "quant-ph". 2012. No. 1210.3270.
Added: September 25, 2016
Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203-1222
We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...
Added: February 28, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Семин С. В., Kurkina O. E., Kurkin A. A. et al., Труды НГТУ им. Р.Е. Алексеева 2012 № 2(95) С. 48-65
Purpose: Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer.
Approach: The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid.
Findings: The full nonlinear numerical modeling of internal wave dynamics ...
Added: October 6, 2012