TY - JOUR

T1 - Bound-state soliton gas as a limit of adiabatically growing integrable turbulence

AU - Agafontsev, Dmitry S.

AU - Gelash, Andrey A.

AU - Mullyadzhanov, Rustam I.

AU - Zakharov, Vladimir E.

N1 - Funding Information:
Simulations have been performed at the Novosibirsk Supercomputer Center (NSU). The work of D.A., A.G. and V.Z. on the main part of the paper (Sections 2 , 3 , 4 , 5.1 , 5.2 ) has been supported by the Russian Science Foundation (Grant No. 19-72-30028 ). A.G. thanks for the support of the Russian Foundation for Basic Research (grant No. 19-31-60028 ) for the work on Section 5.3 and Appendix C . The development of numerical IST methods by R.M. (see Appendix B ) has been supported by the state contract with IT SB RAS, Russia .
Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2023/1

Y1 - 2023/1

N2 - We study numerically the integrable turbulence in the framework of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) of the focusing type using a new approach called the “growing of turbulence”. In this approach, we add a small linear pumping term to the equation and start evolution from statistically homogeneous Gaussian noise. After reaching a certain level of average intensity, we switch off the pumping and examine the resulting integrable turbulence. For sufficiently small initial noise and pumping coefficient, and also for not very wide simulation box (basin length), we observe that the turbulence grows in a universal adiabatic regime, moving successively through the statistically stationary states of the integrable 1D-NLSE, which do not depend on the pumping coefficient, amplitude of the initial noise or basing length. Waiting longer in the growth stage, we transit from weakly nonlinear states to strongly nonlinear ones, characterized by a high frequency of rogue waves. Using the inverse scattering transform (IST) method to monitor the evolution, we observe that the solitonic part of the wavefield becomes dominant even when the (linear) dispersion effects are still leading in the dynamics and with increasing average intensity the wavefield approaches a dense bound-state soliton gas, whose properties are defined by the Fourier spectrum of the initial noise. Regimes deviating from the universal adiabatic growth also lead to solitonic states, but solitons in these states have noticeably different velocities and a significantly wider distribution by amplitude, while the statistics of wavefield indicates a much more frequent appearance of very large waves.

AB - We study numerically the integrable turbulence in the framework of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) of the focusing type using a new approach called the “growing of turbulence”. In this approach, we add a small linear pumping term to the equation and start evolution from statistically homogeneous Gaussian noise. After reaching a certain level of average intensity, we switch off the pumping and examine the resulting integrable turbulence. For sufficiently small initial noise and pumping coefficient, and also for not very wide simulation box (basin length), we observe that the turbulence grows in a universal adiabatic regime, moving successively through the statistically stationary states of the integrable 1D-NLSE, which do not depend on the pumping coefficient, amplitude of the initial noise or basing length. Waiting longer in the growth stage, we transit from weakly nonlinear states to strongly nonlinear ones, characterized by a high frequency of rogue waves. Using the inverse scattering transform (IST) method to monitor the evolution, we observe that the solitonic part of the wavefield becomes dominant even when the (linear) dispersion effects are still leading in the dynamics and with increasing average intensity the wavefield approaches a dense bound-state soliton gas, whose properties are defined by the Fourier spectrum of the initial noise. Regimes deviating from the universal adiabatic growth also lead to solitonic states, but solitons in these states have noticeably different velocities and a significantly wider distribution by amplitude, while the statistics of wavefield indicates a much more frequent appearance of very large waves.

KW - Integrable turbulence

KW - Rogue waves

KW - Solitons

UR - http://www.scopus.com/inward/record.url?scp=85143320955&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/edb7cf77-8b38-3434-90f2-872e6be6801c/

U2 - 10.1016/j.chaos.2022.112951

DO - 10.1016/j.chaos.2022.112951

M3 - Article

AN - SCOPUS:85143320955

VL - 166

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

M1 - 112951

ER -