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SUMMARY:Bound-state soliton gas as a limit of adiabatically growing integr
 able turbulence - Dmitry Agafontsev (P.P. Shirshov Institute of Oceanology
 )
DTSTART:20221020T103000Z
DTEND:20221020T110000Z
UID:TALK182615@talks.cam.ac.uk
DESCRIPTION:We study numerically the integrable turbulence in the framewor
 k of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) of the f
 ocusing type using a new approach called the "growing of turbulence". In t
 his approach\, we add a small linear pumping term to the equation and star
 t evolution from statistically homogeneous Gaussian noise. After reaching 
 a certain level of average intensity\, we switch off the pumping and exami
 ne the resulting integrable turbulence. For sufficiently small initial noi
 se and pumping coefficient\, and also for not very wide simulation box (ba
 sin length)\, we observe that the turbulence grows in a universal adiabati
 c regime\, moving successively through the statistically stationary states
  of the integrable 1D-NLSE\, which do not depend on the pumping coefficien
 t\, amplitude of the initial noise or basing length. Waiting longer in the
  growth stage\, we transit from weakly nonlinear states to strongly nonlin
 ear ones\, characterized by a high frequency of rogue waves. Using the inv
 erse scattering transform (IST) method to monitor the evolution\, we obser
 ve that the solitonic part of the wavefield becomes dominant even when the
  (linear) dispersion effects are still leading in the dynamics and with in
 creasing average intensity the wavefield approaches a dense bound-state so
 liton gas\, whose properties are defined by the Fourier spectrum of initia
 l noise. Regimes deviating from the universal adiabatic growth also lead t
 o solitonic states\, but solitons in these states have noticeably differen
 t velocities and a significantly wider distribution by amplitude\, while t
 he statistics of wavefield indicates a much more frequent appearance of ve
 ry large waves.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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