Shedding and interaction of solitons in imperfect medium
JETP Letters. 2001. Vol. 74. No. 7. P. 391-395.
Kolokolov I., Lebedev V., Chertkov M., Gabitov I.
The propagation of a soliton pattern through one-dimensional medium with weakly disordered dispersion is considered. Solitons, perturbed by this disorder, radiate. The emergence of a long-range interaction between the solitons, mediated by the radiation, is reported. Basic soliton patterns are analyzed. The interaction is triple and is extremely sensitive to the phase mismatch and relative spatial separations within the pattern. This phenomenon is a generic feature of any problem explaining adiabatic evolution of solitons through a medium with frozen disorder.
Research target: Physics
Priority areas: mathematics
, , et al., JETP Letters 2001 Vol. 74 No. 11 P. 608-611
The radiation-mediated interaction of solitons in a one-dimensional nonlinear medium (optical fiber) with birefringent disorder is shown to be independent of the separation between solitons. The effect produces a potentially dangerous contribution to the signal lost. ...
Added: March 5, 2017
, , et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2003 Vol. 67 P. 036615-1-036615-21
The propagation of the soliton pattern through optical fiber with weakly disordered dispersion coefficient is considered. Solitons perturbed by this disorder radiate and, as a consequence, decay. The average radiation profile is found. Emergence of a long-range intrachannel interaction between the solitons ~mediated by this radiation! is reported. We show that soliton in a multisoliton pattern experiences a ...
Added: February 24, 2017
, , et al., EPL 2004 Vol. 66 No. 4 P. 499-502
We study the interplay between amplifier noise and birefringent disorder in the case of strongly nonlinear (soliton) type of transmission in optical fibers. Assuming both noise and disorder to be weak, we evaluate the probability distribution function (PDF) of the Bit-Error-Rate (BER) for the values of BER that are much larger than the typical (average) ...
Added: February 18, 2017
, , et al., Physica D: Nonlinear Phenomena 2004 Vol. 195 P. 1-28
We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger ...
Added: February 12, 2017
Solitons in a third-order nonlinear Schrodinger equation with the pseudo-Raman scattering and spatially decreasing second-order dispersion
, , 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
, , 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
The Peregrine breather on the zero-background limit as the two-soliton degenerate solution: An experimental study
, , et al., Frontiers in Physics 2021 Vol. 9 Article 633549
Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate ...
Added: August 25, 2021
, 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
, , 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
, , , 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
Dynamics of the Davydov-Scott soliton with location or velocity mismatch of its high-frequency component
, , 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
, , et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2001 Vol. 63 No. 025601(R) P. 025601-1-025601-4
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though the noise is weak, we are interested in probabilities of large fluctuations ~generally non-Gaussian! which are beyond perturbation theory. Our method is a development of the instanton formalism ~method of optimal fluctuation! based on a saddle-point approximation in ...
Added: February 23, 2017
, , et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2003 Vol. 68 No. 6 P. 066619 -1-066619 -4
We consider a linear model of optical transmission through a fiber with birefringent disorder in the presence of amplifier noise. Both disorder and noise are assumed to be weak, i.e., the average bit-error rate (BER) is small. The probability distribution function (PDF) of rare violent events leading to the values of BER much larger than ...
Added: February 24, 2017
, , , 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
Solitons in a Third-Order Nonlinear Schrödinger Equation with the Pseudo-Raman Scattering and Spatially Decreasing Second-Order Dispersion
, , 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
, , 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
, , et al., Journal of Lightwave Technology 2004 Vol. 22 No. 4 P. 1155-1168
This paper presents a method that allows evaluating the performance of an optical fiber system where bit errors result from a complex interplay of spontaneous noise generated in optical amplifiers and birefringent disorder of the transmission fiber. We demonstrate that in the presence of temporal fluctuations of birefringence characteristics, the bit-error rate (BER) itself is ...
Added: February 23, 2017
, , Communications in Nonlinear Science and Numerical Simulation 2020 Vol. 85 Article 105220
We introduce a nonlinear Schrödinger equation (NLSE) which combines the pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a non-conservative cubic one with the first spatial derivative, and an external potential, which helps to stabilize solitons against the pseudo-SRS effect. Dynamics of solitons is addressed by means of analytical and numerical methods. The quasi-particle approximation (QPA) for the solitons ...
Added: February 5, 2020
Wave amplification in the framework of forced nonlinear Schrödinger equation: the rogue wave context
, , , 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
, , 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
Солитоны в расширенном нелинейном уравнении Шредингера с псевдорамановским рассеянием и нелинейной дисперсией
, , 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
, Journal of Statistical Mechanics: Theory and Experiment 2020 No. 053301 P. 1-12
We study numerical propagation of energy in a one-dimensional Ding-Dong lattice composed of linear oscillators with elastic collisions. Wave propagation is suppressed by breaking translational symmetry, and we consider three ways to do this: position disorder, mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an ...
Added: October 31, 2020
, , Журнал экспериментальной и теоретической физики 2004 Т. 125 № 2 С. 395-398
Propagation of a light pulse through a weakly inhomogeneous optical fiber is analyzed. The nonlinear envelope equation describing the evolution of polarized pulses is determined by statistical properties of inhomogeneities in the optical fiber. The isotropic Manakov system of equations is shown to be applicable in the presence of high-frequency small-scale defects in the fiber. In the presence ...
Added: February 23, 2017
, Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1-8
We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...
Added: October 26, 2017