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## Dispersionless evolution of inviscid nonlinear pulses

EPL. 2020. Vol. 129. Article 64003.

Isoard M., Kamchatnov A.M., Pavloff N.

We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.

Switzerland : Springer, 2018

The present book gathers chapters from colleagues of A. Ezersky from Russia, especially
those from Nizhny Novgorod Institute of Applied Physics of the Russian Academy
of Science and from France, with whom he has been collaborating on experimental
and theoretical developments.
The book is subdivided into two parts. Part I contains eight chapters related to
nonlinear water waves and Part II ...

Added: October 21, 2018

Slunyaev A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 101 Article 062214

A method of windowed spatiotemporal spectral filtering is proposed to segregate different nonlinear wave components and to calculate the surface of free waves. The dynamic kurtosis (i.e., produced by the free wave component) is shown able to contribute essentially to the abnormally large values of the surface displacement kurtosis, according to the direct numerical simulations of realistic sea ...

Added: June 28, 2020

Pelinovsky E., Ezersky A., Abha N., La Houille Blanche 2016 No. 1 P. 58-65

We have prepared two sets of experiments in a wave flume to model effects occurring in nature and to demonstrate resonance phenomena in laboratory conditions. The first set was performed to investigate non‑linear wave run‑up on the beach caused by harmonic wave maker located at some distance from the shore line. It is revealed that ...

Added: October 29, 2016

Kamchatnov A.M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 99 No. 1 Article 012203

We suggest a method for calculation of parameters of dispersive shock waves in the framework of Whitham modulation theory applied to nonintegrable wave equations with a wide class of initial conditions corresponding to propagation of a pulse into a medium at rest. The method is based on universal applicability of Whitham’s “number of waves conservation ...

Added: February 4, 2021

Kamchatnov A.M., Chaos 2020 Vol. 30 Article 123148

The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the background flow, which interacts with the edge wave packets or the edge solitons. A conjecture about the existence ...

Added: February 4, 2021

Kamchatnov A.M., Chaos 2019 Vol. 29 Article 023106

We discuss the problem of breaking of a nonlinear wave in the process of its propagation into a medium at rest. It is supposed that the profile of the wave is described at the breaking moment by the function (−x) 1/n (x < 0, positive pulse) or −x 1/n (x > 0, negative pulse) of ...

Added: February 4, 2021

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

Камчатнов А. М., Шайкин Д. В., EPL 2021 Vol. 136 Article 40001

We study the evolution of pulses propagating through focusing nonlinear media. A small disturbance of a smooth initial non-uniform pulse amplitude leads to formation of a region of strong nonlinear oscillations. We develop here an asymptotic method for finding the law of motion of the front of this region. The method is based on the conjecture that instability ...

Added: October 20, 2022

Камчатнов А. М., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2022 Vol. 105 Article 044204

Equations for contour dynamics of trough-shaped dark solitons are obtained for the general form of the nonlinearity function. Their self-similar solution which describes the nonlinear stage of the bending instability of dark solitons is studied in detail. ...

Added: October 20, 2022

Slunyaev A., Пелиновский Д. Е., Pelinovsky E., Успехи физических наук 2023 Т. 193 № 2 С. 155-181

Rogue waves are anomalously high waves that may suddenly form on the sea surface. At the dawn of the 21st century, they attracted the interest of researchers, from oceanographers to mathematicians. The review discusses the results of their research: physical mechanisms leading to the generation of anomalously high waves and respective mathematical models, observational data, results of ...

Added: February 13, 2023

Щербак С. А., Lipovskii A., Babich E. S., Journal of Physics: Conference Series 2018 Vol. 1124 No. 5 P. 051028

An analytical study of the second harmonic generation by metal core - dielectric shell spherical nanoparticles was performed. Dependences of the second harmonic intensity on the dielectric shell thickness were calculated. We demonstrated that the thin coating allows tuning surface plasmon resonance wavelength, whereas in presence of the thick shell spatial Mie resonances occur. Estimated ...

Added: December 9, 2020

Gurbatov S., Pelinovsky E., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 No. 1 P. 012207

The paper considers the probability distributions of the nonlinear wave characteristics in nondispersive media
that satisfy the Riemann- and the Kardar-Parisi-Zhang-type equations. By using the Lagrangian and Euler
relations of statistical descriptions, expressions are obtained for the probability density of the Riemann wave
(displacement) integral through the initial probability density of displacement, velocity, and acceleration. The
case of Gaussian ...

Added: July 24, 2020

Kurkina O., Rouvinskaya E., Talipova T. et al., Physica D: Nonlinear Phenomena 2016 Vol. 333 P. 222-234

Internal tidal wave entering shallow waters transforms into an undular bore and this process can be described in the framework of the Gardner equation (extended version of the Korteweg-de Vries equation with both quadratic and cubic nonlinear terms). Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear ...

Added: March 3, 2016

Камчатнов А. М., Иванов С. К., Nonlinear Dynamics 2022 Vol. 108 P. 2505-2512

We consider the modulationally stable version of the Kaup–Boussinesq system which models propagation of onlinear waves in various physical situations. It is shown that the Whitham modulation equations for this model have a new type of solutions which describe trigonometric shock waves. In the Gurevich–Pitaevskii problem of evolution of an initial discontinuity, these solutions correspond to a ...

Added: October 20, 2022

Chervinskii S., Koskinen K., Scherbak S. et al., Physical Review Letters 2018 Vol. 120 No. 11 P. 113902

We study second-harmonic generation from gold nanoislands covered with amorphous titanium oxide
(TiO2) films. As the TiO2 thickness increases, the plasmon resonance of the nanoislands shifts away from the second-harmonic wavelength of 532 nm, diminishing the resonant enhancement of the process at this wavelength. Nevertheless, the second-harmonic signal is enhanced by up to a factor of ...

Added: December 9, 2020

Matveenko S., Bahovadinov M. S., Baranov M. A. et al., Physical Review A: Atomic, Molecular, and Optical physics 2022 Vol. 106 No. 1 Article 013319

We discuss finite-temperature damping of rotons in elongated Bose-condensed dipolar gases, which are in the Thomas-Fermi regime in the tightly confined directions. The presence of many branches of excitations, which can participate in the damping process, is crucial for the Landau damping and results in significant increase of the damping rate. It is found, however, ...

Added: December 13, 2022

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

Ogorodnikov L.L., S.S. Vergeles, Optics Letters 2018 Vol. 43 No. 4 P. 651-654

We study the output emission statistics of a random continuous-wave Raman fiber laser. The signal evolution is governed by a generalized nonlinear Schrödinger equation (NLSE) with inserted gain. The statistics are close to the Rayleigh one, and the deviations are caused by the Kerr nonlinearity. To characterize the deviations, we analytically find the mean of ...

Added: February 8, 2018

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

Kartashova E., Talipova T., Pelinovsky E., Nonlinear Processes in Geophysics 2013 Vol. 20 No. 4 P. 571-580

The nonlinear deformation of long internal waves in the ocean is studied using the dispersionless Gardner equation. The process of nonlinear wave deformation is determined by the signs of the coefficients of the quadratic and cubic nonlinear terms; the breaking time depends only on their absolute values. The explicit formula for the Fourier spectrum of ...

Added: October 15, 2013

Chabchoub A., Hoffmann N., Onorato M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 86 No. 5 P. 156601-1-156601-6

We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrodinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the ...

Added: January 18, 2013

L. F. Calazans de Brito, A. M. Kamchatnov, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 109 No. 1 Article 015102

We consider nonlinear wave structures described by the modified Korteweg–de Vries equation, taking into account a small Burgers viscosity for the case of steplike initial conditions. The Whitham modulation equations are derived, which include the small viscosity as a perturbation. It is shown that for a long enough time of evolution, this small perturbation leads to the ...

Added: February 1, 2024

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

Zhumagulov Y., Vyacheslav D. Neverov, Alexander E. Lukyanov et al., Physical Review B: Condensed Matter and Materials Physics 2022 Vol. 105 No. 11 Article 115436

Second-harmonic generation (SHG) is a well-known nonlinear spectroscopy method to probe electronic
structure, specifically, in transition metal dichalcogenide (TMDC) monolayers. This work investigates the
nonlinear dynamics of a strongly excited TMDC monolayer by solving the time evolution equations for the
density matrix. It is shown that the presence of excitons qualitatively changes the nonlinear dynamics leading,
in particular, to ...

Added: August 26, 2022