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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:About plane periodic waves of the nonlinear SchrÃ¶d
inger equations - L. Miguel Rodrigues (UniversitÃ©
de Rennes 1)
DTSTART;TZID=Europe/London:20220715T140000
DTEND;TZID=Europe/London:20220715T143000
UID:TALK175907AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175907
DESCRIPTION:In a recent contribution\, jointly with Corentin A
udiard (Sorbonne)\, we have obtained a quite exten
sive theory for the stability analysis of plane pe
riodic waves of general Schrö\;dinger equation
s. On one hand\, we put the one-dimensional theory
\, or in other words the stability theory for long
itudinal perturbations\, on a par with the one ava
ilable for systems of Korteweg type\, including re
sults on co-periodic spectral instability\, nonlin
ear co-periodic orbital stability\, side-band spec
tral instability and linearized large-time dynamic
s in relation with modulation theory\, and resolut
ions of all the involved assumptions in both the s
mall-amplitude and large-period regimes.\n \;\
nOn the other hand\, we provide extensions of the
spectral part of the latter to the multi-dimension
al context. Notably\, we provide suitable multi-di
mensional modulation formal 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 this
analysis.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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