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SUMMARY:On the stabilization of breather -type solutions of the  damped hi
 gher order nonlinear Schrödinger equation - Constance Schober (University
  of Central Florida)
DTSTART:20221018T140000Z
DTEND:20221018T143000Z
UID:TALK182543@talks.cam.ac.uk
DESCRIPTION:Spatially periodic breather solutions (SPBs) of the nonlinear 
 Schr&ouml\;dinger (NLS) equation are frequently used to model rogue waves 
 and are typically unstable.In this paper we study the effects of dissipati
 on and higher order nonlinearities on the stabilization of both single and
  multi-mode SPBs in the framework of a damped higher order NLS (HONLS) equ
 ation. We observe the onset of novel instabilities associated with the dev
 elopment of critical states which result from symmetry breaking in the dam
 ped HONLS system. We broaden the Floquet characterization 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 c
 omplex elements of both the periodic and continuous Floquet spectrum. As a
  result the Floquet criteria for the stabilization of a solution of the da
 mped HONLS centers around the elimination of all complex degenerate elemen
 ts of the spectrum.\nFor an initial SPB with a given mode structure\, a pe
 rturbation analysis shows that for short time only the complex double poin
 ts associated with resonant modes split under the damped HONLS while those
  associated with nonresonant modes remain effectively closed. The correspo
 nding damped HONLS numerical experiments corroborate that instabilities as
 sociated with nonresonant modes persist on a longer time scale than the in
 stabilities associated with resonant modes.
LOCATION:Seminar Room 1\, Newton Institute
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