Efim Pelinovsky

• Principal Investigator at Institute of Applied Physics, Russian Academy of Sciences

The present paper is devoted to the study of the dynamics of narrowband wave fields within the nonintegrable Schamel equation, which plays an important role in plasma physics, wave dynamics in meta-materials, and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent realizations of the wave fields, allow...

We investigate the interaction of solitons with an external periodic field within the framework of the modified Korteweg-de Vries (mKdV) equation. In the case of small perturbation a simple dynamical system is used to describe the soliton behaviour. Equilibrium points of this dynamical system are computed when the external force travels at a consta...

The study of Fermi–Pasta–Ulam–Tsingou (FPUT) recurrence is examined within the framework of the Gardner equation. The evolution of harmonic waves is investigated for both positive and negative cubic nonlinearities. It is observed that harmonic waves undergo fission into solitons, which then interact with each other. For positive cubic nonlinearity,...

This paper contributes in the first part to the correct understanding of the linear limit in the Schamel equation (S-equation) from the perspective of structure formation in collisionless plasmas. The corresponding modes near equilibrium turn out to be nonlinear modes of the underlying microscopic Vlasov-Poisson (VP) system for which particle trapp...

In this work, we study the evolution of disturbances within the framework of the Cubic Vortical Whitham (CV-Whitham) equation, considering both positive and negative cubic nonlinearities. This equation plays important role for description of the wave processes in the presence of shear flows. We find well-formed breather-type structures arising from...

Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated using the Benjamin-Ono equation. 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 peak frequency. The expected value of t...

The present article is devoted to the study of the dynamics of narrowband wave fields within the non-integrable Schamel equation, which plays an important role in plasma physics, wave dynamics in meta-materials, and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent realizations of the wave fields, al...

An analysis of internal waves arising in a two-layer fluid during an explosive eruption of an underwater volcano is performed. Processes occurring in the near zone are parameterized by the initial source in the form of a displacement of the water column, as proposed by Le Méhaute (Mehaute, Adv Hydrosci 7:1–79, 1971). Then the linear problem is solv...

The vortical Whitham equation is modeled with quadratic and cubic nonlinearity, satisfying the unidirectional dispersion relation used to describe the propagation of nonlinear waves in the presence of a vertically sheared current of constant vorticity. In this article, we neglect the quadratic nonlinearity to numerically investigate solitary wave i...

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 wav...

Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons interact elastically. However, soliton turbulence can also be a part of non-integrable dynamics, where long-lastin...

Pair soliton interactions play a significant role in the dynamics of soliton turbulence. The interaction of solitons with different polarities is particularly crucial in the context of abnormally large wave formation, often referred to as freak or rogue waves, as these interactions result in an increase in the maximum wave field. In this article, w...

Pair soliton interactions play a significant role in the dynamics of soliton turbulence. The interaction of solitons with different polarities is particularly crucial in the context of abnormally large wave formation, often referred to as freak or rogue waves, as these interactions result in an increase in the maximum wave field. In this article, w...

The functions of the distribution of tsunami wave heights along the eastern coast of Sakhalin Island from sources located along the Kuril Islands are being studied. Known information about the tsunami on Sakhalin is given. Many of them were modeled numerically, which made it possible to assess the hazard of tsunami waves. The present work focuses o...

The data of long-term surface waves measurements with bottom sensors near Sakhalin Island were used to build instrumental probability distributions for exceedance of wave heights. Waves with heights exceeding the significant wave height by more than three times were recorded. Specific features of the observations conducted during the periods of ope...

Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons interact elastically. However, soliton turbulence can also be a part of non-integrable dynamics, where long-lastin...

These authors contributed equally to this work. Abstract: This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin-Ono (BO) equation. The research focuses on analyzing various properties associated with the random wave field, including the transition to...

This article presents a numerical investigation of overtaking collisions between two solitary waves in the context of the Schamel equation. Our study reveals different regimes characterized by the behavior of the wave interactions. In certain regimes, the collisions maintain two well-separated crests consistently over time, while in other regimes,...

The existence of traveling waves in an inhomogeneous medium is a vital problem, the solution of which can help in modeling the wave propagation over long distances. Such waves can be storm waves or tsunami waves in the seas and oceans. The presence of solutions in the form of traveling waves indicates that the wave propagates without reflection and...

This study aims to explore the complex interactions between an internal solitary wave and an external force using the Benjamin-Ono equation as the theoretical framework. The investigation encompasses both asymptotic and numerical approaches. By assuming a small amplitude for the external force, we derive a dynamical system that describes the behavi...

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...

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...

Дан обзор точных решений для гравитационных волн на глубокой воде. Все решения получены в рамках лагранжева описания и являются обобщениями волны Герстнера (в случае неоднородного давления на свободной поверхности и с учетом вращения жидкости). Для каждого типа волн найден вид инвариантов Коши.

In this article, we study nonlinear waves propagating along the background magnetic field in relativistic electron–positron plasmas. Using the reductive perturbation method, we derive a three-dimensional equation describing these waves. When the perturbations do not vary in the directions orthogonal to the background magnetic field this equation re...

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 ex...

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 forc...

The aim of this work is to study asymptotically and numerically the interaction of solitons with an external forcing with variable speed using the forced modified Korteweg-de Vries equation (mKdV). We show that the asymptotic predictions agree well with numerical solutions for forcing with constant speed and linear variable speed. Regarding forcing...

Solving nonlinear differential equations with external forces is important for understanding resonant phenomena in the physics of oscillations. The article analyzes this problem basing on example of an ordinary second-order differential equation of the pendulum type, where the nonlinearity is described by a sinusoidal term. The phase plane of such...

The aim of this work is to study numerically the interaction of large amplitude solitary waves with an external periodic forcing using the forced extended Korteweg-de Vries equation (feKdV). Regarding these interactions, we find that a solitary wave can bounce back and forth remaining close to its initial position when the forcing and the solitary...

Rational solutions of nonlinear evolution equations are considered in the literature as a mathematical image of rogue waves, which are anomalously large waves that occur for a short time. In this work, bounded rational solutions of Gardner-type equations (the extended Korteweg-de Vries equation), when a nonlinear term can be represented as a sum of...

The problem of the existence of traveling waves in inhomogeneous fluid is very important for enabling an explanation of long-distance wave propagations such as tsunamis and storm waves. The present paper discusses new solutions to the variable-coefficient wave equations describing traveling waves in fluid layers of variable depths (1D shallow-water...

We study the stability of one-dimensional solitons propagating in an anisotropic medium. We derived the Kadomtsev-Petviashvili equation for nonlinear waves propagating in an anisotropic medium. By a proper variable substitution this equation reduces either to the KPI or to the KPII equation. In the former case solitons are unstable with respect to...

The paper reports on application of the Gompertz model to describe the growth dynamics of COVID-19 cases during the first wave of the pandemic in different countries. Modeling has been performed for 23 countries: Australia, Austria, Belgium, Brazil, Great Britain, Germany, Denmark, Ireland, Spain, Italy, Canada, China, the Netherlands, Norway, Serb...

To study stationary periodic weakly vortical waves on water (the Gouyon waves), the method of the modified Lagrangian variables is suggested. The wave vorticity Ω is specified as a series in the small steepness parameter ε in the form: Ω=∑n=1∞εn⋅Ωnb , where Ω n are arbitrary functions of the vertical Lagrangian coordinate b. Earlier Gouyon (1958) s...

In this article we study the plasma motion in the transitional layer of a coronal loop randomly driven at one of its footpoints in the thin-tube and thin-boundary-layer (TTTB) approximation. We introduce the average of the square of a random function with respect to time. This average can be considered as the square of the oscillation amplitude of...

We put forward a solution to the initial boundary value (IBV) problem for the nonlinear shallow water system in inclined channels of arbitrary cross section by means of the generalized Carrier–Greenspan hodograph transform (Rybkin et al. in J Fluid Mech, 748:416–432, 2014). Since the Carrier–Greenspan transform, while linearizing the shallow water...

Compactons are studied in the framework of the Korteweg–de Vries (KdV) equation with the sublinear nonlinearity. Compactons represent localized bell-shaped waves of either polarity which propagate to the same direction as waves of the linear KdV equation. Their amplitude and width are inverse proportional to their speed. The energetic stability of...

The role of various long-wave approximations in the description of the wave field and bottom pressure caused by surface waves, and their relation to evolution equations are being considered. In the framework of the linear theory, these approximations are being tested on the well-known exact solution for the wave spectral amplitudes and pressure var...

It is generally known that the Drake Passage is difficult for navigation; frequent storms occur there, strong winds blow, and huge sea waves are generated. Differentiating storm waves and rogue waves is often difficult. This article provides information about the observations of rogue waves and possible mechanisms for their generation in the Antarc...

Compactons are studied in the framework of the Korteweg--de Vries (KdV) equation with the sublinear nonlinearity. Compactons represent localized bell-shaped waves of either polarity which propagate to the same direction as waves of the linear KdV equation. Their amplitude and width are inverse proportional to their speed. The energetic stability of...

Purpose. Investigation of the storm surge in Korsakov in the southern part of the Sakhalin Island on November 15, 2019 and comparison of the results of its numerical simulation with the data of in situ measurements constitute the aim of the article. Methods and Results. In situ measurements of the storm surge in Korsakov (the Sakhalin region) were...

We put forward a solution to the initial boundary value (IBV) problem for the nonlinear shallow water system in inclined channels of arbitrary cross-section by means of the generalized Carrier-Greenspan hodograph transform (Rybkin et al., 2014). Since the Carrier-Greenspan transform, while linearizing the shallow water system, seriously entangles t...

In this paper we study dispersive enhancement of a wave train in systems described by the fractional Korteweg–de Vries-type equations of the form u t + α n u n u x + β m ( D m { u } ) x = 0 , D m { u } = − | k | m u ( k ) where the operator D m { u } is written in the Fourier space, α n , β m are arbitrary constants and n , m being rational numbers...

The existence of traveling waves in a strongly inhomogeneous magnetized plasma is studied. It is shown that under certain conditions for characteristics of the medium, the waves do not reflect from inhomogeneities, although their amplitude and phase vary in space. Such non-reflective waves are found mathematically as solutions of wave equations wit...

Cases of “freak waves” that occurred in the period from 2011 to 2018 and information on which is currently available are analyzed. In total, 210 cases of abnormally large waves that caused destruction, loss of human life, and injury are identified. A map of events is compiled, the sea depth for each case (deep/shallow waters, the coast) is determin...

In this paper we study dispersive enhancement of a wave train in systems described by the fractional Korteweg-de Vries-type equations of the form u t + α n u n u x + β m (D m {u}) x = 0, D m {u} = −|k| m u(k) where the operator D m {u} is written in the Fourier space, α n , β m are arbitrary constants and n, m being rational numbers (positive or ne...

Possibilities of forecasting of a tsunami characteristics for areas with small base of historical tsunami are discussed. The PTHA method (Probabilistic Tsunami Hazard Assessment), which cornerstone the statistical analysis of real and predictive earthquakes which number is rather big, with the subsequent calculation of waves of a Tsunami from possi...

Direct numerical simulations of irregular unidirectional nonlinear wave evolution are performed within the framework of the Korteweg–de Vries equation for bimodal wave spectra model cases. The additional wave system co-existence effect on the evolution of the wave statistical characteristics and spectral shapes, and also on the attained equilibrium...

The nonlinear problem of long wave run-up on a plane beach in a presence of a tide is solved within the shallow water theory using the Carrier-Greenspan approach. The exact solution of the nonlinear problem for wave run-up height is found as a function of the incident wave amplitude. Influence of tide on characteristics of wave run-up on a beach is...

The influence of counter interaction of nonlinear wave in the shallow water has been studied. It is shown that such an interaction leads to a change in the phase of propagation of the main wave, which is forced to propagate along the flow induced by the counter-propagating wave. Estimates of the height of the non-breaking wave at the moment of inte...

Tsunami forecast possibilities for areas with a small base of historical tsunamis have been discussed using the Probabilistic Tsunami Hazard Assessment (PTHA) method, which is based on a statistical analysis of a sufficiently large number of real and predictive earthquakes with a subsequent calculation of possible tsunami waves. This method has bee...

The influence of nonlinear interaction of oppositely directed nonlinear waves in a shallow basin is studied theoretically and numerically within the nonlinear theory of shallow water. It is shown that this interaction leads to a change in the phase of propagation of the main wave, which is forced to propagate along the flow induced by the oncoming...

Дано описание математических моделей, применяемых при решении проблемы генерации и распространения волн цунами от различных источников: подводных землетрясений, оползневых движений в воде и резких изменений атмосферных условий (метеоцунами). В их основе лежит известная нелинейная теория «мелкой воды» и ее дисперсионные обобщения (плановые уравнения...

Numerical modeling of a 28'th September Tsunami on the Sulawesi Island (Indonesia) is executed. It is shown that observed distribution of a Tsunami heights in the extensive territory can be explained direct action of a strong earthquake, and in a center zone (the district of Palu) - submarine landslide.

In this Letter we study modular Hopf equation of the form u t +|u|u x =0and obtain explicit form of its exact solution in the Fourier space, for the particular initial conditions of a sine wave. This solution exists for a finite time before wave breaking. We also demonstrate the qualitative difference between the Fourier spectra of the modular and...

Numerical simulation of a tsunami from September 28, 2018, on Sulawesi Island (Indonesia) is carried out. It is shown that the observed distribution of tsunami heights within a large area can be explained by the direct effect of a strong earthquake, whereas in the source zone (area of the city of Palu) it was produced by an underwater landslide.

The dynamics of wave ensembles in shallow water is studied within the framework of the nonlinear dispersive Korteweg – de Vries (KdV) equation by numerical simulation. Bimodal wave systems whose energy is distributed over two spectral domains are considered: the “additional” lobe which corresponds to the system of longer or shorter waves is added t...

In this Letter we study modular Korteweg-de Vries equation (KdV) of the form u t + |u| u x + u xxx = 0 and obtain explicit form of its exact solution the dispersionless limit in the Fourier space. This solution exists for a finite time before wave breaking. We also demonstrate the qualitative difference between the Fourier spectra of the modular an...

On September 28th, 2018, a powerful earthquake (Mw 7.5) struck the Island of Sulawesi in Indonesia. The earthquake was followed by a destructive and deadly tsunami that hit the Bay of Palu. A UNESCO international tsunami survey team responded to the disaster and surveyed 125 km of coastline along the Palu Bay up to the earthquake epicentre region....

We study the statistical moments of the soliton gas (mean field, variance, skewness, and kurtosis), which is described within the framework of the Gardner equation with negative cubic nonlinearity. The influence of the limiting (thick or table-like) soliton on the statistical moments of the soliton gas is considered. It is shown to be substantial i...

Our present study is devoted to the constructive study of the modulational instability for the Korteweg-de Vries (KdV)-family of equations u t + s u p u x + u x x x (here s = ± 1 and p > 0 is an arbitrary integer). For deducing the conditions of the instability, we first computed the nonlinear corrections to the frequency of the Stokes wave and the...

The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves are concerned. The results are compared with the solution of the full potential Euler equations and with the low...

The universal mechanism of modulation instability (MI) has been discovered first for the Nonlinear Schr\"{o}dinger equation (NLS) and is well studied in the frame of the higher order NLS equations. Recent studies demonstrated by pure existence theorems that also the higher order Korteweg-de Vries (KdV) equations might possess the MI. In this Letter...

The universal mechanism of modulation instability (MI) has been discovered first for the Nonlinear Schrödinger equation (NLS) and is well studied in the frame of the higher order NLS equations. Recent studies demonstrated by pure existence theorems that also the higher order Korteweg–de Vries (KdV) equations might possess the MI. In this Letter we...

The paper presents results of numerical simulations of freely rising solid spheres in a viscous fluid. The diameter of spheres was 5 mm, 7 mm, 10 mm, and 20 mm, and the corresponding Reynolds numbers varies in the interval 1400<Re<10100. It has been found that the free rise path varies, as the Galileo number increases. The paper describes the princ...

We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier–Greenspan transformation (Carrier and Greenspan (1957) [9]). We use a Taylor series approximation to deal with the difficulty associated with the initial conditions given on a curve in the transformed space. This extends...

The long wave run-up on two types of slopes is investigated numerically within the framework of nonlinear shallow water theory using the CLAWPACK software. One of the slopes represents a plane slope widely used in the laboratory and numerical experiments; the second is the so-called “non-reflecting” slope (h ~ x4/3, where h is the basin depth and x...

This contribution is focused on the semidiurnal internal tide in the Barents Sea generated north of the critical latitude (74.5° N). The study is based on the numerical modeling of internal wave generation and dynamics using of the Euler 2D equations for incompressible stratified fluid. The study site is located between Svalbard and the Franz-Victo...

Modeling of tsunamis in glacial fjords prompts us to evaluate applicability of the cross-sectionally averaged nonlinear shallow water equations to model propagation and runup of long waves in asymmetrical bays and also in fjords with two heads. We utilize the Tuck-Hwang transformation, initially introduced for the plane beaches and currently genera...

The original version of this article unfortunately contained mistakes. Entries were incorrect in the reference list and also their citations in the last sentence on p. 297, right-hand column. © 2017 Springer International Publishing AG, part of Springer Nature

A nonlinear Schrödinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously vortical infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is shown that the modulational instabili...

Observation data on the September 5, 1971, earthquake that occurred near the Moneron Island (Sakhalin) have been analyzed and a numerical simulation of the tsunami induced by this earthquake is conducted. The tsunami source identified in this study indicates that the observational data are in good agreement with the results of calculations performe...