?
Распространение уединенных внутренних волн в двухслойном океане переменной глубины
Известия РАН. Физика атмосферы и океана. 2015. Т. 51. № 1. С. 103-112.
Талипова Т. Г., Kurkina O. E., Rouvinskaya E., Pelinovsky E.
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
Marshirov V. V., Литейное производство 2013 № 5 С. 36-39
Using the finite difference method developed model of solidification. The model includes the change in the physical properties of materials on the temperature, the existence of phase transitions and complex boundary conditions. Using the model was performed comparison the influence of materials, boundary and initial conditions to the changing temperature fields of castings and molds. ...
Added: May 31, 2013
Gaydukov R., Сибирский журнал вычислительной математики 2022 Т. 15 № 2 С. 97-109
A viscous liquid flow along a semi-infinite plate with small periodic irregularities on the surface was
considered for large Reynolds numbers. The flow near the plate is described by Prandtl equations with
induced pressure which are non-classical PDE, because they contain a limiting term. The main goal is to
construct a numerical algorithm for solving these equations with ...
Added: June 10, 2020
Tyugin D. Y., Averbukh E. L., Kurkina O. E. et al., Современная наука: исследования, идеи, результаты, технологии 2012 № 2(10) С. 318-323
В данной статье представлен программный комплекс, предназначенный для численного моделирования распространения антропогенних загрязнений и примесей в поле внутренних волн. Модель расчета примесей основана на уравнении баланса поверхностной концентрации, она реализована с помощью неявного метода конечных разностей и протестирована на ряде аналитических решений уравнения адвективно-диффузионного переноса примесей. Поле внутренних волн задается на основе уравнения Гарднера-Островского с ...
Added: October 8, 2012
Blyakhman L. G., Morozov V. P., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2016 № 3 (114) С. 9-15
Цель работы: Исследована динамика двухкомпонентных (векторных) солитонов Давыдова-Скотта(ДС) при пространственно-скоростном рассогласовании высокочастотных (ВЧ) и низкочастотных (НЧ) компонент. Рассмотрение проведено в рамках Захаровского типа системы двух связанных уравнений для ВЧ и НЧ поля. В этой системе ВЧ поле описывается линейным уравнением Шредингера с переменным во времени и пространстве потенциалом, вызванным НЧ компонентой. НЧ компонента в этой ...
Added: October 5, 2016
Aseeva N., Gromov E., Tyutin V. V., Известия высших учебных заведений. Радиофизика 2013 Т. 56 № 3 С. 173-183
We consider the soliton dynamics in terms of the extended nonlinear Schrödinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. ...
Added: August 27, 2013
Pelinovsky E., Родин А., Известия РАН. Физика атмосферы и океана 2013 Т. 49 № 5 С. 595-600
Получено аналитическое решение нелинейных уравнений мелкой воды, определяющее высоты волн цунами, выходящих из очага. В очаге задано начальное смещение уровня воды и распределе ние скоростей частиц. Численное решение показало, что аналитические оценки хорошо совпадают с рассчитанными в широком диапазоне изменения характеристик очага, даже если выходящие из очага волны обрушиваются. ...
Added: October 15, 2013
Mikheev A. V., Теория. Практика. Инновации 2017 № 9 (21)
In this paper we consider the calculation of a dynamical system described by a second-order differential equation in which a fundamental system of solutions consisting of functions of exponential type is replaced by bounded functions of the Verhulst model. The time dependence of the forces acting on the dynamical system is analyzed, and the obtained ...
Added: September 6, 2017
Gaydukov R., Danilov V., Наноструктуры. Математическая физика и моделирование 2016 Т. 15 № 1 С. 5-102
We study the existence conditions for a double-deck structure of a boundary layer in typical problems of incompressible fluid flow along surfaces with small irregularities (periodic or localized) for large Reynolds number. We obtain characteristic scales (a power of a small parameter included in a solution) which lead to the double-deck structure, and we obtain ...
Added: September 27, 2016
Averbukh E. L., Kurkina O. E., Kurkin A. A. et al., Экологические системы и приборы 2012 № 10 С. 63-72
Рассматривается распространение и трансформация уединенных внутренних волн и их поверхностные проявления без учета и с учетом вращения Земли в рамках уравнений Гарднера и Гарднера – Островского в горизонтально-однородном и неоднородном (как по плотности, так и по глубине) стратифицированном бассейне. Динамика пленок поверхностно активных веществ в поле внутренних волн была промоделирована на основе уравнения баланса поверхностной ...
Added: October 8, 2012
Kurkina O., Rouvinskaya E., Talipova T. et al., Physica D: Nonlinear Phenomena 2016 Vol. 333 P. 222-234
Internal tidal wave entering shallow waters transforms into an undular bore and this process can be described in the framework of the Gardner equation (extended version of the Korteweg-de Vries equation with both quadratic and cubic nonlinear terms). Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear ...
Added: March 3, 2016
Danilov V., Gaydukov R., Vadim Kretov et al., IEEE Transactions on Electron Devices 2014 Vol. 61 No. 12 P. 4232-4239
This paper presents the results of mathematical modeling of heat transfer in the field emission process in a conic cathode of small dimensions with its possible melting considered. It is shown that the possibility of melting is determined by the cathode vertex angle. The melting is modeled in the framework of the phase field system ...
Added: October 24, 2014
Blyakhman L. G., Gromov E., Malomed B. A. et al., Chaos, Solitons and Fractals 2018 No. 117 P. 264-268
The dynamics of two-component solitons with a small spatial displacement of the high-frequency (HF) component relative to the low-frequency (LF) one is investigated in the framework of the Zakharov-type system. In this system, the evolution of the HF field is governed by a linear Schrödinger equation with the potential generated by the LF field, while ...
Added: November 12, 2018
Pelinovsky E., Ezersky A., Abha N., La Houille Blanche 2016 No. 1 P. 58-65
We have prepared two sets of experiments in a wave flume to model effects occurring in nature and to demonstrate resonance phenomena in laboratory conditions. The first set was performed to investigate non‑linear wave run‑up on the beach caused by harmonic wave maker located at some distance from the shore line. It is revealed that ...
Added: October 29, 2016
Aseeva N., Gromov E., Tyutin V. V., Radiophysics and Quantum Electronics 2013 Vol. 56 No. 3 P. 157-166
We consider the soliton dynamics in terms of the extended nonlinear Schr¨odinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. ...
Added: October 8, 2013
Aseeva N., Gromov E., Tyutin V. V., Chaos 2013 Vol. 23 No. 1 P. 013143-1-013143-6
Solitons dynamics in the frame of the extended nonlinear Schrodinger equation taking into account space stimulated Raman scattering (SSRS), synchronic spatial variation of inhomogeneous second-order dispersion (SOD), and self-phase modulation (SPM) is considered both analytically and numerically. Compensation of soliton Raman self–wave number down shift by synchronically increasing SOD and SPM is shown. Analytical soliton ...
Added: April 4, 2013
Danilov V., Rudnev V., Gaydukov R. et al., М. : Научно-техническое издательство «Горячая линия – Телеком», 2014
A new mathematical model of heat transfer in silicon field emission pointed cathode of small dimensions is constructed which permits taking its partial melting into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type problems. The approach used by the authors is not purely mathematical but ...
Added: September 23, 2014
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
Талипова Т. Г., Kurkina O. E., Терлецкая Е. В. et al., Экологические системы и приборы 2014 № 3 С. 26-38
Necessity of study of the internal waves of large amplitude in the Barents Sea related to their possible catastrophic effects on
offshore platforms, powerful transport sediments and bottom erosion, which invariably affects on the overall environmental
situation. In this paper, numerical simulation of the generation and propagation of internal waves in the Barents Sea in
the framework of ...
Added: May 13, 2014
Gurbatov S., Pelinovsky E., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 No. 1 P. 012207
The paper considers the probability distributions of the nonlinear wave characteristics in nondispersive media
that satisfy the Riemann- and the Kardar-Parisi-Zhang-type equations. By using the Lagrangian and Euler
relations of statistical descriptions, expressions are obtained for the probability density of the Riemann wave
(displacement) integral through the initial probability density of displacement, velocity, and acceleration. The
case of Gaussian ...
Added: July 24, 2020
O. Kurkina, T. Talipova, E. Pelinovsky et al., Journal of Coastal Research 2011 No. SI64 P. 2042-2047
The geographical and seasonal distributions of kinematic and nonlinear parametersof long internal waves obtained on a base of GDEM climatology in the Baltic Sea region are examined. The considered parameters (phase speed of long internal wave, dispersion, quadratic and cubicnonlinearity parameters) of the weakly-nonlinear Korteweg-de Vries-type models (in particular, Gardner model), can be used for ...
Added: October 11, 2012
Chabchoub A., Hoffmann N., Onorato M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 86 No. 5 P. 156601-1-156601-6
We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrodinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the ...
Added: January 18, 2013
Aseeva N., Blyakhman L. G., Logvinova K. V. et al., Труды НГТУ им. Р.Е. Алексеева 2013 № 3(100) С. 37-46
Цель работы: Рассмотрена динамика солитонов в рамках расширенного нелинейного уравнения Шредингера. Учтено как индуцированное рассеяние высокочастотных волн на затухающих низкочастотных волнах, так и неоднородность линейной дисперсии второго порядка.
Научный подход: Исследование проведено как численно, так и аналитически.
Результат: Показано, что смещение пространственного спектра солитона в длинноволновую область, обусловленного индуцированным рассеянием, компенсируется убывающей дисперсией, смещающей спектр солитона в ...
Added: September 24, 2013
Pelinovsky E., Kurkin A. A., Kurkina O. E. et al., Известия РАН. Физика атмосферы и океана 2014 Т. 50 № 6 С. 714-722
Трансформация пакета внутренних волн при его распространении на португальском шельфе изучалась во время международного эксперимента EU MAST II MORENA в 1994 г. В статье представлены результаты моделирования динамики этого пакета для гидрологических условий по трассе распространения. Моделирование проводилось на основе обобщенного уравнения Гарднера, включающего неоднородность гидрологии, вращение Земли и диссипацию в придонном пограничном слое. Обсуждаются ...
Added: November 18, 2013