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Бегущие волны в недиспергирующих сильно неоднородных средах
Доклады Российской академии наук. Физика, технические науки (ранее - Доклады Академии Наук. Физика). 2022. Т. 506. № 2. С. 46–51.
Pelinovsky E., Капцов О. В.
Methods to obtain solutions describing traveling waves in strongly inhomogeneous media are discussed
within a linear wave equation with a variable speed (speed of sound). It is shown that there is a wide
range of propagation speed variations that allow for the existence of waves that do not reflect despite the
strong inhomogeneity of the medium. In this case, the shape of the wave and its characteristics change with
distance. These waves can transfer energy over long distances without loss.
Keywords: Волновое уравнение
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
Белоусов Н. М., Черепанов Л. К., Деркачов С. Э. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Муравьев М. Ю., Annales mathématiques du Québec (Канада) 2025
Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Interpreting his approach in terms of differential forms permits to generalize these results to a much broader context. The spectrum of the absolute boundary problem for ...
Added: May 6, 2026
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 2026
Morozov E. V., Demin A. S., Borovitskaya I. V. et al., Inorganic Materials: Applied Research 2026 Vol. 17 No. 3 P. 619–626
This article presents the results of experiments on the impact of powerful pulsed ion-plasma and
electron flows generated in the working chamber of the Plasma Focus PF-5M installation during each highvoltage
discharge on a model aluminum alloy B95. It is shown that the general characteristics of the alloy’s
damage upon exposure to pulsed flows of helium ions (HI) ...
Added: May 4, 2026
Монахова Э. А., Монахов О. Г., Rzaev E. et al., Прикладная дискретная математика 2026 Т. 71 С. 112–127
В настоящей работе исследовано совместное конструирование топологий семейств оптимальных по диаметру циркулянтных сетей $C(N; \pm 1, \pm s_2)$ и реализуемых для них оптимальных алгоритмов маршрутизации сложности $O(1)$. Предлагаемый алгоритм маршрутизации основан на использовании масштабируемых параметров $L$-образных шаблонов плотной укладки графов на плоскости для семейств оптимальных сетей.
Определены аналитические формулы зависимости этих параметров от диаметра графов семейств ...
Added: May 4, 2026
Dudakov S., Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 12 P. 6092–6102
We study the additive theory of arbitrary figures in linear spaces, that is, the theory of
addition extended to sets of vectors. Our main result is the following: if a linear space is infinite,
then the additive theory of figures admits interpreting second-order arithmetic and, therefore, it has
such or higher degree of undecidability. For countably infinite spaces, ...
Added: May 1, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Ponomarev A., Aleksandrov N., Plasma Physics Reports 2026 Vol. 52 No. 3 P. 367–378
An approximate method for calculating drift velocity and other kinetic coefficients of heavy ions
in a light gas is generalized to gaseous mixtures. Obtained equations are used to calculate the mobilities of
and ions, as well as rate constants for inelastic ion–molecule processes with these ions in helium with
small additions of O2 under an electric field. Calculated ...
Added: April 27, 2026
Domrin V. I., Malova H. V., V. Yu. Popov et al., Cosmic Research 2026 Vol. 64 No. 2 P. 238–252
During magnetospheric perturbations a relatively thin current sheet with thickness about several
proton gyroradii forms in the Earth’s magnetotail. In a framework of the kinetic model describing current
sheet thinning in the magnetotail, the processes of its formation are investigated depending on the normal
magnetic field magnitude which affects both the current sheet structure and particle dynamics within ...
Added: April 27, 2026
Tsareva O. O., Malova H. V., V. Yu. Popov et al., Plasma Physics Reports 2026 Vol. 52 No. 2 P. 179–185
The influence of asymmetry of plasma sources on the structure and spatial localization of a superthin
current sheet (STCS) supported by demagnetized electrons is studied using a self-consistent model. The
simulation takes into account the presence of a single plasma source in the northern hemisphere, which
makes the plasma flow asymmetric. It is demonstrated that the asymmetry of ...
Added: April 27, 2026
П.А.Беспалов, О.Н. Савина, Геомагнетизм и аэрономия 2025 Т. 65 № 5 С. 620–628
Several basic models of frequency dynamics in quasi-periodic VLF emissions with spectral form repetition
periods from 10 to 300 s are considered. In all cases, we are talking about manifestations of cyclotron instability
of electron radiation belts thet are well described within the framework of the plasma magnetospheric maser
theory based an the averaged self-consistent system of quasi-linear ...
Added: April 25, 2026
Beklaryan A., Бекларян Л. А., Журнал вычислительной математики и математической физики 2022 Т. 62 № 6 С. 933–950
The existence of a family of bounded soliton solutions for a finite-difference analogue of the wave equation with a general nonlinear potential is proved. The proof is based on a formalism establishing a one-to-one correspondence between soliton solutions of an infinite-dimensional dynamical system and solutions of a family of functional differential equations of the pointwise type. A key ...
Added: May 30, 2022
Beklaryan L. A., Beklaryan A., Computational Mathematics and Mathematical Physics 2021 Vol. 61 No. 12 P. 1980–1994
The existence of a family of bounded soliton solutions for a finite-difference wave equation with a quadratic potential is established. The proof is based on a formalism establishing a one-to-one correspondence between the soliton solutions of an infinite-dimensional dynamical system and the solutions of a family of functional differential equations of the pointwise type. A ...
Added: January 14, 2022
Бекларян Л. А., Beklaryan A., Журнал вычислительной математики и математической физики 2021 Т. 61 № 12 С. 2024–2039
The existence of a family of bounded soliton solutions for a finite difference wave equation with a quadratic potential is established. The proof is carried out within the framework of a formalism that establishes a one-to-one correspondence between soliton solutions of an infinite-dimensional dynamical system and solutions of a family of pointwise functional differential equations. For ...
Added: November 1, 2021
Maslov V., Теоретическая и математическая физика 2021 Т. 206 № 3 С. 448–452
We consider the construction of asymptotic solutions of linear equations related to equations of classical mechanics: the Hamilton–Jacobi equation and the transport equation. We show that these methods and also the theory of the mechanics of an infinitely narrow beam as a whole can be applied to some objects in bioenergy if the thin organic ...
Added: July 14, 2021
Zlotnik A., Kireeva O., / Series arXiv "math". 2020. No. arXiv:2011.14104v2[math.NA].
We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the classical Numerov approach and alternative technique based on averaging of the equation, together with further necessary improvements of the arising scheme for $n\geq 2$. The ...
Added: December 1, 2020
Petropavlovsky S., Цынков С. В., Журнал вычислительной математики и математической физики 2020 Т. 60 № 4 С. 725–737
A boundary method for simulation of wave propagation in 3D is proposed. The approach relies on the method of difference potentials and Huygens'principle allowing for an update of the solution only on the boundaries of a scatterer/ ...
Added: April 13, 2020
Romanov I., Шамаев А. С., Известия РАН. Теория и системы управления 2019 № 1 С. 109–116
The boundary controllability of oscillations of a plane membrane is studied. The magnitude
of the control is bounded. The controllability problem of driving the membrane to rest is considered.
The method of proof proposed in this paper can be applied to any dimension but only the two-dimensional case is considered for simplicity. ...
Added: April 30, 2019
Горшков А. А., Ossadtchi A., Фрадков А. Л., Информационно-управляющие системы 2017 Т. 5 № 90
Постановка проблемы: пространственное разрешение электроэнцефалографии/магнитоэнцефалографии зависит от метода решения обратной задачи, которая в силу фундаментальных физических причин является некорректно поставленной и имеет бесконечно большое количество решений. В последние несколько лет появились новые свидетельства о том, что нейрональная активность распространяется по коре в соответствии с волновым паттерном, характеризуемым некоторым направлением и скоростью распространения волны. Новые данные ...
Added: April 21, 2018
Vexler B., Zlotnik A., Trautmann P., Comptes Rendus Mathematique 2018 Vol. 356 No. 5 P. 523–531
The paper deals with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces of either measure-valued functions or vector measures. Bilinear finite element discretizations are constructed and their stability and error analysis is accomplished. ...
Added: April 8, 2017
Trautmann P., Vexler B., Zlotnik A., Mathematical Control and Related Fields 2018 Vol. 8 No. 2 P. 411–449
This work is concerned with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L^2(I,\mathcal M(\Omega))$ or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$, $\alpha>0$. We construct and study three-level ...
Added: April 8, 2017
Trautmann P., Vexler B., Zlotnik A., / Series "Working papers by Cornell University". 2017. No. 1702.00362.
This work is concerned with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L^2(I,\mathcal M(\Omega))$
or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$, $\alpha>0$. We construct and study three-level in time bilinear ...
Added: February 2, 2017