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Outage probability for soliton transmission
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) value. The PDF tail that describes probability of the system outage shows log-normal shape, strongly dependent on the fiber length. We also discuss a simple timing shift technique capable of the outage compensation.
Kolokolov I., Lebedev V., Chertkov M. 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
Kolokolov I., Lebedev V., Chertkov M. 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
Kolokolov I., Lebedev V., Chertkov M. et al., JETP Letters 2001 Vol. 74 No. 7 P. 391-395
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 ...
Added: March 4, 2017
Kolokolov I., Lebedev V., Chertkov M. 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
I.Kolokolov, Lebedev V., Chertkov M. 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
Kolokolov I., Lebedev V., Falkovich G. 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
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. 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
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
Kolokolov I., Lebedev V., Chertkov M. et al., Optics Letters 2003 Vol. 28 No. 22 P. 2159-2161
We study the dependence on fiber birefringence of the bit-error rate (BER) caused by amplifier noise in a
linear optical fiber telecommunication system. We show that the probability-distribution function of the BER
obtained by averaging over many realizations of birefringent disorder has an extended tail that corresponds to
anomalously large values of BER. We specifically discuss the dependence ...
Added: February 23, 2017
Kolokolov I., Турицын К. С., 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
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
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.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
Kolokolov I., Lebedev V., Turitsyn S. K. 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
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
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
Gromov E.M., Malomed B. A., 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
Kolokolov I., Lebedev V., Chertkov M. et al., Optics Express 2003 Vol. 11 No. 14 P. 1607-1612
Fluctuations of Bit-Error-Rate (BER) stimulated by birefringent
disorder in an optical fiber system are found to be strong. The effect may not
be analyzed in terms of the average BER but rather requires analyzing the
Probability Distribution Function (PDF) of BER. We report the emergence
of the extremely extended algebraic-like tail of the PDF, corresponding to
anomalously large values of ...
Added: February 24, 2017
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
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
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
Окубо Ю. undefined., 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
Andrew G. Semenov, Zaikin A., Physical Review B: Condensed Matter and Materials Physics 2013 Vol. 88 No. 5 P. 054505-1-054505-10
We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current ...
Added: February 9, 2015