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SUMMARY:Periodic and double periodic waves in NLS: existence and stability
  - Dmitry Pelinovsky (McMaster University)
DTSTART:20220823T100000Z
DTEND:20220823T110000Z
UID:TALK177437@talks.cam.ac.uk
DESCRIPTION:I will explain how to compute the instability rates for the do
 uble-periodic solutions to the cubic NLS (nonlinear Schr&ouml\;dinger) equ
 ation by using the Lax linear equations. The wave function modulus of the 
 double periodic solutions is periodic both in space and time coordinates\;
  such solutions generalize the standing periodic waves which have the time
 -independent and space-periodic wave function modulus.\nSimilar to other w
 aves in the NLS equation\, the double-periodic solutions are spectrally un
 stable and this instability is related to the bands of the Lax spectrum ou
 tside the imaginary axis. A simple numerical method is used to compute the
  unstable spectrum and to compare the instability rates of the double-peri
 odic solutions with those of the standing periodic waves.
LOCATION:Seminar Room 2\, Newton Institute
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