Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStrongly interacting soliton gas and formation of rogue waves
301
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study numerically the properties of (statistically) homogeneous soliton gas depending on soliton density (proportional to number of solitons per unit length) and soliton velocities, in the framework of the focusing one-dimensional Nonlinear Schr{o}dinger (NLS) equation. In order to model such gas we use N-soliton solutions (N-SS) with $Nsim 100$, which we generate with specific implementation of the dressing method combined with 100-digits arithmetics. We examine the major statistical characteristics, in particular the kinetic and potential energies, the kurtosis, the wave-action spectrum and the probability density function (PDF) of wave intensity. We show that in the case of small soliton density the kinetic and potential energies, as well as the kurtosis, are very well described by the analytical relations derived without taking into account soliton interactions. With increasing soliton density and velocities, soliton interactions enhance, and we observe increasing deviations from these relations leading to increased absolute values for all of these three characteristics. The wave-action spectrum is smooth, decays close to exponentially at large wavenumbers and widens with increasing soliton density and velocities. The PDF of wave intensity deviates from the exponential (Rayleigh) PDF drastically for rarefied soliton gas, transforming much closer to it at densities corresponding to essential interaction between the solitons. Rogue waves emerging in soliton gas are multi-soliton collisions, and yet some of them have spatial profiles very similar to those of the Peregrine solutions of different orders. We present example of three-soliton collision, for which even the temporal behavior of the maximal amplitude is very well approximated by the Peregrine solution of the second order.
rate research
Read More
In this brief report we study numerically the spontaneous emergence of rogue waves in (i) modulationally unstable plane wave at its long-time statistically stationary state and (ii) bound-state multi-soliton solutions representing the solitonic model of this state [Gelash et al, PRL 123, 234102 (2019)]. Focusing our analysis on the cohort of the largest rogue waves, we find their practically identical dynamical and statistical properties for both systems, that strongly suggests that the main mechanism of rogue wave formation for the modulational instability case is multi-soliton interaction. Additionally, we demonstrate that most of the largest rogue waves are very well approximated -- simultaneously in space and in time -- by the amplitude-scaled rational breather solution of the second order.
We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrodinger (NLS) equation with the initial condition in the form of a rectangular barrier (a box). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains --- the dispersive dam break flows --- generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.
We study numerically the integrable turbulence developing from strongly nonlinear partially coherent waves, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. We find that shortly after the beginning of motion the turbulence enters a state characterized by a very slow evolution of statistics (the quasi-stationary state - QSS), and we concentrate on the detailed examination of the basic statistical functions in this state depending on the shape and the width of the initial spectrum. In particular, we show that the probability density function (PDF) of wavefield intensity is nearly independent of the initial spectrum and is very well approximated by a certain Bessel function representing an integral of the product of two exponential distributions. The PDF corresponds to the value of the second-order moment of intensity equal to 4, indicating enhanced generation of rogue waves. All waves of large amplitude that we have studied are very well approximated - both in space and in time - by the rational breather solutions of either the first (the Peregrine breather), or the second orders.
We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schroedinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue wave like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.
Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schrodinger equation is often used to model rogue waves; it is an envelope description of plane waves and admits the so-called Pergerine and Kuznetov-Ma soliton solutions. However, in deep water waves and certain electromagnetic systems where there are two significant transverse dimensions, the 2+1 hyperbolic nonlinear Schrodinger equation is the appropriate wave envelope description. Here we show that these rogue wave solutions suffer from strong transverse instability at long and short frequencies. Moreover, the stability of the Peregrine soliton is found to coincide with that of the background plane wave. These results indicate that, when applicable, transverse dimensions must be taken into account when investigating rogue wave pheneomena.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
