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## Statistics of soliton-bearing systems with additive noise

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 the path integral. We first
solve a fundamental problem of soliton statistics governed by a noisy nonlinear Schro¨dinger equation. We then
apply our method to optical soliton transmission systems using signal control elements ~filters and amplitude
and phase modulators!.

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., 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

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

Kolokolov I., Chertkov M., Chernyak V. 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

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., 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

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

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

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., 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

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., Chertkov M., Gabitov I. et al., Journal of the Optical Society of America 2004 Vol. 21 No. 3 P. 486-498

Polarization mode dispersion is the effect of signal broadening in a fiber with birefringent disorder. The disorder, frozen into the fiber, is characterized by the so-called vector of birefringence (VB). In a linear medium a pulse broadens as the two principal states of polarization split. It is well-known that, under the action of short-correlated disorder, ...

Added: February 13, 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

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

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

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

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

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

Slunyaev A., Кокорина А. В., Water Waves, Springer 2019 P. 1-20

The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for accurate ...

Added: October 13, 2019

Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203-1222

We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...

Added: February 28, 2013

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Prazdnichnykh A., Glazov M., Ren L. et al., Physical Review B: Condensed Matter and Materials Physics 2021 Vol. 103 No. 8 P. 085302-1-085302-12

The exciton valley dynamics in van der Waals heterostructures with transition metal dichalcogenide monolayers is driven by the long-range exchange interaction between the electron and the hole in the exciton. It couples the states active in the opposite circular polarizations resulting in the longitudinal-transverse splitting of excitons propagating in the monolayer plane. Here we study ...

Added: March 5, 2021