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Перспективы использования солитонов для передачи информации в каналах связи .
С. 128–131.
Tarasov P., Pervukhin D.
In book
М.: Издательский дом НИУ ВШЭ, 2017.
Flamarion M., Didenkulova E., Pelinovsky E., Physics Letters A 2026 Vol. 598 Article 132218
In this letter, bipolar solitary wave interactions in the Schamel equation are revisited numerically. Two simulation settings are considered: repeated collisions in a periodic domain, and the interaction of a positive solitary wave with a train of negative polarity solitary waves of equal amplitude. In the first case, when the amplitudes are comparable, the larger ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Flamarion M., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 208 No. 3 Article 118271
Two-solitary-wave interactions are investigated within the fourth-order generalized Korteweg–
de Vries equation. This equation is closely related to the classical Korteweg–de Vries equation
but includes a quartic nonlinear term. We show that, although collisions between two solitary
waves are not perfectly elastic, only a small amount of radiation is generated during the
interaction. This allows a clear characterization of ...
Added: March 22, 2026
Kamchatnov A.M., Suleimanov B. I., Tsoy E. N., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2025 Vol. 111 No. 6 Article 064203
In this paper, we derive equations for the dynamics of ring dark solitons in an expanding cloud of a twodimensional Bose-Einstein condensate. Assuming that the soliton’s width is much smaller than its radius, we obtain the Hamilton equations for its evolution. Then they are transformed into the Newton equation, which is more convenient for applications. The general ...
Added: February 11, 2026
Shaykin D. V., A.M. Kamchatnov, Physical Review A: Atomic, Molecular, and Optical physics 2025 Vol. 112 No. 6 Article 063511
We develop the theory of dispersive shock waves in optical fibers for the case of long-distance propagation of optical pulses, when the small Raman effect stabilizes the profile of the shock. The Whitham modulation equations are derived as the basis for the Gurevich-Pitaevskii approach to the analytical theory of such shocks. We show that the wave variables at ...
Added: February 11, 2026
dos Santos G., Calasans de Brito L. F., Gammal A. et al., Physical Review A: Atomic, Molecular, and Optical physics 2025 Vol. 112 No. 3 Article 033318
A supersonic flow past an obstacle can generate a rich variety of wave excitations. This paper investigates, both analytically and numerically, two types of excitations generated by the flow of a Lee-Huang-Yang quantum fluid past an obstacle: linear radiation and oblique dark solitons. We show that wave crests of linear radiation can be accurately described by the proper ...
Added: February 11, 2026
Gromov E., Malomed B. A., Physics Letters A 2026 Vol. 567 Article 131219
We introduce an extended nonlinear Lugiato-Lefever equation (LLE) with the pseudo-stimulated-Raman-scattering (pseudo-SRS) cubic term, linear damping/gain, and spatial inhomogeneous (weekly or strongly localized) pump. The LLE is derived, in the extended adiabatic approximation, from the underlying Zakharov’s system (ZS), which includes a viscosity term acting on its low-frequency (LF) component and the pump supporting the ...
Added: November 28, 2025
Flamarion M. V., Pelinovsky E., Didenkulova E., Applied Mathematical Modelling 2025 Vol. 144 Article 116092
Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated via the Benjamin-Ono equation, which models internal waves in a two-layer fluid. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly distributed, while its frequency spectrum has a Gaussian shape centered at a ...
Added: March 23, 2025
Pelinovsky E., Gurbatov S., Chaos, Solitons and Fractals 2025 Vol. 192 Article 116056
The statistical properties of a sequence of spaced solitons and compactons (soliton gas) with random amplitudes
and phases are studied based on the example of solitary waves – solutions of the generalized Korteweg-de Vries
equation with power nonlinearity (including fractional nonlinearity). Such sequences are used to specify initial
conditions in problems of modeling soliton turbulence. It is shown ...
Added: January 25, 2025
Chekmazov S., Ksenz A., Andrei M. Ionov et al., Scientific Reports 2024 Vol. 14 Article 2331
Sb is a three-dimensional Peierls insulator. The Peierls instability gives rise to doubling of the translational period along the [111] direction and alternating van der Waals and covalent bonding between (111) atomic planes. At the (111) surface of Sb, the Peierls condition is violated, which in theory can give rise to properties differing from the ...
Added: December 15, 2024
Ostrovsky L., E. Pelinovsky, Shrira V. et al., Chaos 2024 Vol. 34 No. 6 Article 062101
The review is concerned with solitary waves and other localized structures in the systems described by a variety of generalizations of the Korteweg–de Vries (KdV) equation. Among the topics we focus upon are “radiating solitons,” the generic structures made of soliton-like pulses, and oscillating tails. We also review the properties of solitary waves in the generalized KdV ...
Added: June 14, 2024
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
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
Пиковский А., Rosenau P., Nonlinearity 2021 Vol. 34 P. 5872–5896
We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka–Volterra chain. Their deceptively simple form supports a very rich family of complex solitary patterns. Some of these patterns are also found in the quasi-continuum ...
Added: December 3, 2021
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
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
Камчатнов А. М., Успехи физических наук 2021 Т. 191 № 1 С. 52–87
We present an introduction to the theory of dispersive shock waves in the framework of the approach proposed by Gurevich and Pitaevskii (Zh. Eksp. Teor. Fiz., Vol. 65, p. 590 (1973) [Sov. Phys. JETP, Vol. 38, p. 291 (1974)]) based on Whitham’s theory of modulation of nonlinear waves. We explain how Whitham equations for a ...
Added: October 14, 2021
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