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SUMMARY:Miles Wheeler (University of Bath)
DTSTART:20201020T190000Z
DTEND:20201020T200000Z
DTSTAMP:20260423T021447Z
UID:ONEPAS/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ONEPAS/6/">S
 olitary waves and fronts</a>\nby Miles Wheeler (University of Bath) as par
 t of Online Northeast PDE and Analysis Seminar\n\n\nAbstract\nI will give 
 a general introduction to the theory of solitary water waves\, that is tra
 veling waves whose surfaces converge to some asymptotic height at infinity
 . In many respects\, the theory for solitary waves is more difficult and m
 ore subtle than that for periodic waves. Yet in other ways the problem is 
 much simpler\, and indeed many results for solitary waves are stronger tha
 n their periodic counterparts. \n\nBeginning with the linear theory\, or p
 erhaps more accurately the <em>lack</em> of a linear theory\, I will expla
 in how small-amplitude waves can be rigorously constructed via a center ma
 nifold reduction. Next I will collect a series of results which together g
 uarantee that any solitary wave\, regardless of amplitude\, is symmetric a
 nd decreasing about a central crest and travels at a “supercritical” s
 peed $c>\\sqrt{gd}$. Finally\, I will explain how the significant obstacle
 s to applying global bifurcation techniques can be overcome by taking adva
 ntage of the above properties together with the <em>nonexistence</em> of f
 ront-type solutions. This approach is surprisingly robust\, and has recent
 ly been generalized to apply to front-type solutions in addition to solita
 ry waves.\n
LOCATION:https://researchseminars.org/talk/ONEPAS/6/
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