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Soliton interactions with an external forcing: The modified Korteweg–de Vries framework
Chaos, Solitons and Fractals. 2022. Vol. 165. Article 112889.
Flamarion M. V., Pelinovsky E.
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 find regimes in which the solitons are trapped at the
external forcing and its amplitude increases or decreases in time depending on whether the forcing accelerates
or decelerates.
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
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
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
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
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
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
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
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., 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
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
Gromov E., Tyutin V. V., Aseeva N., Труды НГТУ им. Р.Е. Алексеева 2012 № 4(97) С. 61-73
Исследована динамика солитонов огибающей в рамках расширенного уравнения Шредингера. Научный подход: Исследование проведено как численно, так и аналитически. В аналитической теории замкну-тую систему шести интегралов исходного модельного уравнения удалось свести к системе двух обыкновенных дифференциальных уравнений, в которой анализировалась структура фазового пространства.
Результат: Показано, что смещение волнового числа в длинноволновую область, обусловленное индуцирован-ным рассеянием Рамана может ...
Added: January 25, 2013
Kachulin D., Dyachenko A., Gelash A., Fluids 2019 Vol. 4 No. 2 Article 83
We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water—breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow ...
Added: October 22, 2022
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
Pelinovsky E., Шургалина Екатерина Геннадьевна, Известия высших учебных заведений. Радиофизика 2014 Т. 57 № 10 С. 825-833
Изучается взаимодействие двух солитонов разной полярности в рамках модифицированного уравнения Кортевега—де Вриза. Рассмотрено три типа взаимодействия солитонов: обменный и обгонный (для положительных солитонов) и поглощательно-излучательный (для разнополярных солитонов). Подробно исследованы особенности взаимодействия солитонов. Поскольку взаимодействие солитонов является элементарным актом солитонной турбулентности, нами изучены обычно рассматриваемые в теории турбулентности моменты волнового поля с первого по четвёртый ...
Added: March 12, 2015
Bienaime T., Isoard M., Fontaine Q. et al., Physical Review Letters 2021 Vol. 126 Article 183901
We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge of the shock, as well as the location of the nonlinear oscillations are well described ...
Added: October 14, 2021
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
Gromov E.M., Malomed B. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2015 Vol. 92 No. 6 P. 062926-1-062926-7
Dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped low-frequency (LF) internal waves. The drive gives rise to a convective (but not absolute) instability in the system. The resulting NLSE ...
Added: December 5, 2015
Flamarion M., Pelinovsky E., Chaos, Solitons and Fractals 2023 Vol. 174 Article 113799
This study aims to investigate the interactions of solitons with an external force within the framework of the
Schamel equation, both asymptotically and numerically. By utilizing asymptotic expansions, we demonstrate
that the soliton interaction can be approximated by a dynamical system that involves the soliton amplitude
and its crest position. To solve the Schamel equation, we employ a ...
Added: July 20, 2023
Solitary Wave Interactions with an External Periodic Force: The Extended Korteweg-de Vries Framework
Flamarion M. V., Pelinovsky E., Mathematics 2022 Vol. 10 No. 23 Article 4538
In this work we asymptotically and numerically studied the interaction of large amplitude
solitary waves with an external periodic force using the forced extended Korteweg-de Vries equation
(feKdV). Regarding these interactions, we found three types of regimes depending on the amplitude
of the solitary wave and how its speed and the speed of the external force are related. ...
Added: December 1, 2022
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
Wave amplification in the framework of forced nonlinear Schrödinger equation: the rogue wave context
Pelinovsky E., Slunyaev A., Sergeeva A., Physica D: Nonlinear Phenomena 2015 Vol. 303 P. 18-27
Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrödinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble. The slow ...
Added: August 4, 2015
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
Kamchatnov A., Shaykin D. V., Physics of Fluids 2021 Vol. 33 Article 052120
We consider propagation of high-frequency wave packets along a smooth evolving background flow whose evolution is described by a simple-wave type of solutions of hydrodynamic equations. In geometrical optics approximation, the motion of the wave packet obeys the Hamilton equations with the dispersion law playing the role of the Hamiltonian. This Hamiltonian depends also on ...
Added: October 14, 2021
Kamchatnov A.M., L. F. Calazans de Brito, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2021 Vol. 104 Article 054203
We show that the number of solitons produced from an arbitrary initial pulse of the simple wave type can be calculated analytically if its evolution is governed by a generalized nonlinear Schroedinger equation provided this number is large enough. The final result generalizes the asymptotic formula derived for completely integrable nonlinear wave equations like the standard NLS equation ...
Added: January 17, 2022