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SUMMARY:Solitons in external fields - Maciej Zworski (UC Berkeley)
DTSTART:20091207T160000Z
DTEND:20091207T170000Z
UID:TALK20926@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:Solitons are the remarkably stable solitary wave solutions to 
 certain nonlinear evolution equations\, such as the nonlinear Schroedinger
  equation (NLS) or the Korteveg-de Vries equation (KdV). They also enjoy a
  remarkable sociological stability by being of interest to applied mathema
 ticians\, PDE experts\, algebraic geometers\, and representation theorists
 . The particle-like behaviour of solitons is visible when external potenti
 als are added to the original equations. That means that in addition to se
 lf-interaction modeled by the nonlinearity\, an external field is applied 
 to the solitary waves. That can result in different kinds of phenomena inv
 olving one or more solitons. I will describe results obtained in collabora
 tion with Justin Holmer\, and with Justin Holmer and Galina Perelman\, on 
 solitons for NLS and mKdV interacting with slowly varying external fields 
 (semiclassical regime)\, and with highly localized impurities (delta funct
 ion potentials). The mathematical results are strikingly confirmed in nume
 rical experiments which also suggest many open questions.
LOCATION:CMS\, MR15
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