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SUMMARY:Wave patterns generated by large-amplitude rogue waves and their u
 niversal character - Deniz Bilman (University of Cincinnati)
DTSTART:20221012T143000Z
DTEND:20221012T153000Z
UID:TALK183206@talks.cam.ac.uk
DESCRIPTION:It is known from our recent work that both fundamental rogue w
 ave solutions (with Peter Miller and Liming Ling) and multi-pole soliton s
 olutions (with Robert Buckingham) of the nonlinear Schr&ouml\;dinger equat
 ion exhibit the same universal asymptotic behavior in the limit of large o
 rder in a shrinking region near the peak amplitude point\, despite the qui
 te different boundary conditions these solutions satisfy at infinity. We r
 eview these results and show that this profile arises universally from arb
 itrary background fields. We then show how rogue waves and solitons of arb
 itrary orders can be placed within a common analytical framework in which 
 the "order" becomes a continuous parameter\, allowing one to tune continuo
 usly between types of solutions satisfying different boundary conditions. 
 &nbsp\;In this framework\, solitons and rogue waves of increasing integer 
 orders alternate as the continuous order parameter increases. &nbsp\;We sh
 ow that in a bounded region of the space-time of size proportional to the 
 order\, these solutions all appear to be the same when the order is large.
  &nbsp\;However\, in the unbounded complementary region one sees qualitati
 vely different asymptotic behavior along different sequences. This is join
 t work with Peter Miller (U. Michigan).
LOCATION:Seminar Room 2\, Newton Institute
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