TY - JOUR

T1 - Strongly interacting soliton gas and formation of rogue waves

AU - Gelash, A. A.

AU - Agafontsev, D. S.

N1 - Publisher Copyright: © 2018 American Physical Society.

PY - 2018/10/18

Y1 - 2018/10/18

N2 - 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 Schrödinger (NLS) equation. To model such gas we use N-soliton solutions (N-SS) with N∼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 wavefield 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 multisoliton 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.

AB - 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 Schrödinger (NLS) equation. To model such gas we use N-soliton solutions (N-SS) with N∼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 wavefield 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 multisoliton 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.

KW - NONLINEAR SCHRODINGER-EQUATION

KW - INTEGRABLE SYSTEMS

KW - MODULATION INSTABILITY

KW - OPTICAL-FIBERS

KW - TURBULENCE

KW - TRAINS

UR - http://www.scopus.com/inward/record.url?scp=85055172310&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.98.042210

DO - 10.1103/PhysRevE.98.042210

M3 - Article

AN - SCOPUS:85055172310

VL - 98

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 042210

ER -