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## Динамика солитонов Давыдова-Скотта при пространственно-скоростном смещении компонент

Труды НГТУ им. Р.Е. Алексеева. 2016. № 3 (114). С. 9-15.

Priority areas:
mathematics

Language:
Russian

Blyakhman L. G., Gromov E., Onosova I. V. et al., Physics Letters A 2017 Vol. 381 No. 17 P. 1490-1492

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger ...

Added: February 3, 2017

Evgeny Gromov, Malomed B., Chaos 2017 Vol. 27 No. 11 P. 113107-1-13107-13

New two-component soliton solutions of the coupled high-frequency (HF) - low-frequency (LF) system, based on Schrödinger - Korteweg - de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a ...

Added: October 24, 2017

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

Abrashkin A. A., Gromov E., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2010 № 1 (80) С. 36-42

Propagation of the short vector envelope solitons in a inhomogeneous medium with linear potential in coupled third–order nonlinear Shrodinger equations frame is considered. Explicit vector soliton solution is obtained. The explicit solution for the solitons trajectories is studied. In particular cases this solitons solution can be reduced as to the short scalar soliton solution on ...

Added: May 21, 2012

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

Aseeva N., Blyakhman L. G., Gromov E. et al., Труды НГТУ им. Р.Е. Алексеева 2016 № 2 С. 9-16

Цель работы: Рассмотрена динамика солитонов в рамках расширенного нелинейного уравнения Шредингера, учитывающего псевдо-рамановское рассеяние (рассеяние на затухание низкочастотных волнах), нелинейную дисперсию и пространственную неоднородность дисперсии второго порядка.
Результат: Показано, что при наличии нелинейной дисперсии сдвиг вниз спектра волновых чисел солитона, вызванный псевдо-рамановским рассеянием, может быть компенсирован сдвигом спектра вверх, вызванным пространственным уменьшением дисперсии второго порядка. ...

Added: June 24, 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., Onosova I. V. et al., JETP Letters 2016 Vol. 103 No. 10 P. 737-741

Evolution of solitons is addressed in the framework of a third-order nonlinear Schrodinger 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 underlying ...

Added: May 4, 2016

Gromov E.M., Malomed B. A., Physica Scripta 2015 Vol. 90 No. 6 P. 068021-1-068021-6

Dynamics of Langmuir solitons is considered in plasmas with spatially inhomogeneous electron temperature. An underlying Zakharov-type system of two unidirectional equations for the Langmuir and ion-sound fields is reduced to an inhomogeneous nonlinear Schrödinger equation (NLSE) with spatial variation of the second-order dispersion (SOD) and self-phase modulation (SPM) coefficients, induced by the spatially inhomogeneous profile ...

Added: April 25, 2015

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

Savina O. N., Gromov E., Tyutin V. V., Геомагнетизм и аэрономия 2015 Т. 55 № 5 С. 675-679

The possibility of the existence of the solitary internal gravity waves on the Earth's thermosphere heights is discussed. Analytical results are obtained with local approximation weak
nonisothermal atmosphere. For internal gravity waves is derived Korteweg-de Vries equation with the heterogeneity, nonlinearity and dissipation. Theoretical
results are used to interpret the basic parameters of solitary traveling ionospheric disturbances ...

Added: July 2, 2015

Gromov E., Solycheva O. M., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2011 № 1 (86) С. 44-52

In the frame of the third-order nonlinear wave dispersion theory the equation of motion of a vector wave packets mass center taken in to account arbitrary inhomogeneity profile is obtained. As short vector wave packets localized motion as infinite motion is shown. Short vector wave packets localizations area can be as bigger as smaller in ...

Added: May 21, 2012

Pelinovsky E., Talipova T., Soomere T., Physica D: Nonlinear Phenomena 2021 Vol. 419 No. 5 Article 132785

We analyze the main properties of soliton solutions to the generalized KdV equation u_t +[F (u)]_x+u_xxx
= 0, where the leading term F (u) ∼ qu^α, α > 0, q ∈ R. The far field of such solitons may have
three options. For q > 0 and α > 1 the analysis re-confirmed that all traveling solitons ...

Added: February 13, 2021

O.N. Savina, E.M. Gromov, V.V. Tyutin, Geomagnetism and Aeronomy 2015 Vol. 55 No. 5 P. 658-662

The possibility of the existence of a solitary internal gravity wave at heights of the Earth’s thermosphere is considered. Analytical results were obtained in local approximation with weak nonisothermality of the atmosphere. For internal gravity waves, the Korteweg–de Vries equation was derived and studied with allowance for inhomogeneity, nonlinearity, and dissipation. The theoretical results were ...

Added: October 23, 2015

Gromov Evgeny, Malomed B., Chaos 2016 Vol. 26 No. 12 P. 123118-1-123118-10

One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schrödinger equation (NLSE) for intense HF waves to the Boussinesq (Bq) or Korteweg - de Vries (KdV) equation for the LF component through quadratic terms. The systems apply, ...

Added: November 26, 2016

Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2022 Vol. 165 Article 112889

The aim of this work is to study asymptotically and numerically the interaction of solitons with an external
forcing with a variable speed using the forced modified Korteweg–de Vries equation (mKdV). We show that the
asymptotic predictions agree well with numerical solutions for forcings with constant speed and linear variable
speed. Regarding forcing with linear variable speed, we ...

Added: November 19, 2022

Aseeva N.V., Gromov E.M., Tyutin V.V., Radiophysics and Quantum Electronics 2015 Vol. 58 No. 3 P. 209-215

Evolution of solitons is addressed in the framework of an extended nonlinear Schrödinger equation (NLSE), including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. In the present context, it is induced by the underlying interaction of the high-frequency ...

Added: May 7, 2015

Aseeva N., Gromov E., Tyutin V. V., Известия высших учебных заведений. Радиофизика 2015 Т. 58 № 3 С. 227-234

Evolution of solitons is addressed in the framework of an extended nonlinear Schrödinger equation (NLSE), including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. In the present context, it is induced by the underlying interaction of the high-frequency ...

Added: December 9, 2014

Gromov E., Morozov V. P., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2010 № 4 (83) С. 40-49

The interaction of short single-component vector solitons in the frame of the coupled third–order nonlinear Schrodinger equations taking into account third–order linear dispersion, self–stepping, self–stimulated Ramanscattering, cross–stepping and cross–stimulated Raman-scattering terms is considered. Conditions of reflection and propagation of the solitons through each other and also the condition of oscillator interaction (vector breather) are obtained. ...

Added: May 21, 2012

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

Pelinovsky E., E.G. Shurgalina, Sergeeva A. et al., Physical Letters A 2013 Vol. 377 No. 1 P. 272-275

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) ...

Added: January 18, 2013

Oshmarina O. E., Averbukh E. L., Kurkin A. A., Труды НГТУ им. Р.Е. Алексеева 2010 № 2(81) С. 49-56

In the present work the results of different scenario of the cliff of Cape Canaille hypothetic collapse (South of France) are presented. Three scenarios were considered: falling of one block, falling of several blocks in one time and debris flow avalanche. The analysis of the entire scenario was done. ...

Added: November 5, 2012

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

Семенякин Н. С., Gamayun O., Journal of Physics A: Mathematical and Theoretical 2016 Vol. 49 No. 335201 P. 1-23

We take a soliton solution of a classical non-linear integrable equation and quench (suddenly change) its non-linearity parameter. For that we multiply the amplitude or the width of a soliton by a numerical factor η and take the obtained profile as a new initial condition. We find the values of η for which the post-quench ...

Added: April 4, 2018