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SUMMARY:About plane periodic waves of the nonlinear Schrödinger equations
  - L. Miguel Rodrigues (Université de Rennes 1)
DTSTART:20220715T130000Z
DTEND:20220715T133000Z
UID:TALK175907@talks.cam.ac.uk
DESCRIPTION:In a recent contribution\, jointly with Corentin Audiard (Sorb
 onne)\, we have obtained a quite extensive theory for the stability analys
 is of plane periodic waves of general Schr&ouml\;dinger equations. On one 
 hand\, we put the one-dimensional theory\, or in other words the stability
  theory for longitudinal perturbations\, on a par with the one available f
 or systems of Korteweg type\, including results on co-periodic spectral in
 stability\, nonlinear co-periodic orbital stability\, side-band spectral i
 nstability and linearized large-time dynamics in relation with modulation 
 theory\, and resolutions of all the involved assumptions in both the small
 -amplitude and large-period regimes.\n&nbsp\;\nOn the other hand\, we prov
 ide extensions of the spectral part of the latter to the multi-dimensional
  context. Notably\, we provide suitable multi-dimensional modulation forma
 l asymptotics\, validate those at the spectral level and use them to prove
  that waves are always spectrally unstable in both the small-amplitude and
  the large-period regimes. The present talk shall expound some parts of th
 is analysis.
LOCATION:Seminar Room 1\, Newton Institute
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