TY - JOUR

T1 - Intermittency in generalized NLS equation with focusing six-wave interactions

AU - Agafontsev, D. S.

AU - Zakharov, V. E.

N1 - Funding Information:
The authors thank E. Kuznetsov for valuable discussions concerning this publication, M. Fedoruk for access to and V. Kalyuzhny for assistance with Novosibirsk Supercomputer Center. This work was done in the framework of RSF grant 14-22-00174 , supported by the programs “Fundamental problems of nonlinear dynamics” and the leading scientific schools of Russian Federation, and RFBR grants 12-01-00943-a , 12-05-92004-NNS_a .
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2015/10/23

Y1 - 2015/10/23

N2 - We study numerically the statistics of waves for generalized one-dimensional Nonlinear Schrödinger (NLS) equation that takes into account focusing six-wave interactions, dumping and pumping terms. We demonstrate the universal behavior of this system for the region of parameters when six-wave interactions term affects significantly only the largest waves. In particular, in the statistically steady state of this system the probability density function (PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large waves, with characteristic "fat tail" decaying with amplitude |Ψ| close to ?(-γ|Ψ|), where γ>0 is constant. The corresponding non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in the absence of six-wave interactions, and increases with six-wave coupling coefficient.

AB - We study numerically the statistics of waves for generalized one-dimensional Nonlinear Schrödinger (NLS) equation that takes into account focusing six-wave interactions, dumping and pumping terms. We demonstrate the universal behavior of this system for the region of parameters when six-wave interactions term affects significantly only the largest waves. In particular, in the statistically steady state of this system the probability density function (PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large waves, with characteristic "fat tail" decaying with amplitude |Ψ| close to ?(-γ|Ψ|), where γ>0 is constant. The corresponding non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in the absence of six-wave interactions, and increases with six-wave coupling coefficient.

KW - Generalized NLS equation

KW - Intermittency

KW - Rogue waves

KW - Statistics

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=84940450657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940450657&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2015.05.042

DO - 10.1016/j.physleta.2015.05.042

M3 - Article

AN - SCOPUS:84940450657

VL - 379

SP - 2586

EP - 2590

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 40-41

ER -