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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the stabilization of breather -type solutions o
f the damped higher order nonlinear SchrÃ¶dinger e
quation - Constance Schober (University of Central
Florida)
DTSTART;TZID=Europe/London:20221018T150000
DTEND;TZID=Europe/London:20221018T153000
UID:TALK182543AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/182543
DESCRIPTION:Spatially periodic breather solutions (SPBs) of th
e nonlinear Schrö\;dinger (NLS) equation are f
requently used to model rogue waves and are typica
lly unstable.In this paper we study the effects of
dissipation and higher order nonlinearities on th
e stabilization of both single and multi-mode SPBs
in the framework of a damped higher order NLS (HO
NLS) equation. We observe the onset of novel insta
bilities associated with the development of critic
al states which result from symmetry breaking in t
he damped HONLS system. We broaden the Floquet cha
racterization of instabilities of solutions of the
NLS equation\, using an even 3-phase solution of
the NLS as an example\, to show instabilities are
associated with degenerate complex elements of bot
h the periodic and continuous Floquet spectrum. As
a result the Floquet criteria for the stabilizati
on of a solution of the damped HONLS centers aroun
d the elimination of all complex degenerate elemen
ts of the spectrum.\nFor an initial SPB with a giv
en mode structure\, a perturbation analysis shows
that for short time only the complex double points
associated with resonant modes split under the da
mped HONLS while those associated with nonresonant
modes remain effectively closed. The correspondin
g damped HONLS numerical experiments corroborate t
hat instabilities associated with nonresonant mode
s persist on a longer time scale than the instabil
ities associated with resonant modes.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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