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## Волны Герстнера и их обобщения в гидродинамике и геофизике.

Physics-Uspekhi. 2022. Т. 192. № 5. С. 491-506.

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, rotation, varying pressure on the free surface, stratiécation, compressibility, and background êows. Waves on a rotating Earth are studied in the f-plane approximation, and, in the near-equatorial region, also in the beta-plane approximation. The êows are described in Lagrangian variables. For all waves in the absence of background êows, the trajectories of liquid particles are circles, as in the Gerstner wave (hence, their common nameìGerstner-like).

Publication based on the results of:

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

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

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

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

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

М.: Издательство математико-механического факультета МГУ, 2009

В настоящий сборник вошли аннотации докладов участников XVI международной конференции «Ломоносов» по секции «Математика и механика». ...

Added: February 4, 2013

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

М.: ВИНИТИ РАН, 1985

Added: November 30, 2020

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

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

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

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

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

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

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

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

Journal of High Energy Physics 2012 Vol. 1210

The reduction of the duality invariant approach to M-theory by a U-duality group valued
Scherk-Schwarz twist is considered. We show that all gaugings of SUGRA can be obtained
by dimensional reduction of the extended space. ...

Added: October 20, 2014

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

Нелинейная динамика 2017 Т. 13 № 3 С. 399-412

В статье, используя методы теории динамических систем Морса–Смейла, авторы рассматривают топологическую структуру для точечно-зарядной модели магнитного поля областей фотосферы. Для произвольного количества зарядов (безотносительно к их местоположению) и не предполагая потенциальности поля <span data-mathml="B⃗ (следовательно, не используя конкретных формул), авторы приводят оценки, связывающие количества зарядов определенного типа с количеством нуль-точек. Для граничных оценок описывается топологическая структура магнитного ...

Added: October 12, 2017

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

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

All joint von Neumann measurements on a quantum state admit a quasi-classical probability model / . 2012. No. 1210.3270.

Added: September 25, 2016

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

Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019