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SUMMARY:Nonlinear damped spatially periodic breathers and the emergence of
  soliton-like rogue waves - Constance Schober (University of Central Flori
 da)
DTSTART:20220907T093000Z
DTEND:20220907T103000Z
UID:TALK177839@talks.cam.ac.uk
DESCRIPTION:The spatially periodic breather solutions (SPBs) of the nonlin
 ear Schr&ouml\;dinger equation\, prominent in modeling rogue waves\, are u
 nstable.\nIn this talk we numerically examine the routes to stability of t
 he SPBs and related rogue wave activity in the framework of a nonlinear da
 mped higher order nonlinear Schr&ouml\;dinger (NLD-HONLS) equation.\nThe N
 LD-HONLS solutions are initialized with single-mode and two-mode SPB data 
 at different stages of their development.\nThe Floquet spectral theory of 
 the NLS equation is applied to interpret and provide a characterization of
  the perturbed dynamics in terms of nearby solutions of the NLS equation. 
 A broad categorization of the routes to stability of the SPBs is determine
 d. Novel behavior related to the effects of nonlinear damping is obtained:
  tiny bands of complex spectrum develop in the Floquet decomposition of th
 e NLD-HONLS data\, indicating the breakup of the SPB into either a one or 
 two ``soliton-like'' structure.\nFor solutions initialized in the early to
  middle stage of the development of the modulational instability\, we find
  that all the rogue waves in the NLD-HONLS flow occur when the spectrum is
  in a one or two soliton-like configuration.\nWhen the solutions are initi
 alized as the modulational instability is saturating\, rogue waves may occ
 ur when the spectrum is not in a soliton-like state.\nAnother distinctive 
 feature of the nonlinear damped dynamics is that the growth of instabiliti
 es can be delayed and expressed at higher order due to permanent frequency
  downshifting.
LOCATION:Seminar Room 1\, Newton Institute
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