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SUMMARY:Solitons and breathers in a periodic wave field
DTSTART;VALUE=DATE-TIME:20180321T151500Z
DTEND;VALUE=DATE-TIME:20180321T161500Z
DTSTAMP;VALUE=DATE-TIME:20211022T223153Z
UID:indico-event-3381@indico.math.cnrs.fr
DESCRIPTION:Résumé : The complete integrability of the nonlinear Schrodi
nger equation (NLSE) via inverse scattering transform enables the decompos
ition of the initial conditions into elementary nonlinear modes : the spat
ially localized solitons/breathers and continuous spectrum waves and quasi
-periodic finite gap solutions. Numerical simulations of the NLSE statisti
cs always imply periodic boundary conditions. However\, when the size of t
he periodic box is large the existence of localized solitons/breathters is
possible. Such solitons/breathers under periodic boundary conditions corr
espond to the case of very narrow eigenvalue gaps. To study the role of so
litons in the dynamics and statistics of a periodic wave field we create a
gas of solitons of high density. We use a special stable numerical scheme
to generate statistical ensembles of 128 strongly interacting solitons\,
i.e. solve the inverse scattering problem for the high number of discrete
eigenvalues. Then we use this ensembles as initial conditions for numerica
l simulations in a large numerical box with periodic boundary conditions a
nd study statistics of the obtained uniform strongly interacting soliton g
as. We also study the role of breathers in the development of modulation i
nstability from randomly perturbed quasimonochromatic plane wave. We solve
the Zakharov-Shabat eigenvalue problem with high numerical accuracy and d
emonstrate typical eigenvalue portraits that reveal the coexistence of fin
ite gap quasiperiodic waves and spatially localized breathers.\n\nhttps://
indico.math.cnrs.fr/event/3381/
LOCATION:IMB A318
URL:https://indico.math.cnrs.fr/event/3381/
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