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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Singularities of Burgersâ€™ equation in the complex
plane - Scott McCue (Queensland University of Tech
nology)
DTSTART;TZID=Europe/London:20221101T112000
DTEND;TZID=Europe/London:20221101T121000
UID:TALK185192AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/185192
DESCRIPTION:Following on from previous work\, we analyse solut
ions to Burgers&rsquo\; equation in the complex pl
ane\, concentrating on the dynamics of the complex
singularities and their relationship to the solut
ion on the real line. We use a variety of tools\,
including matched asymptotic expansions\, exponent
ial asymptotics\, exact solutions\, steepest desce
nts and rational approximations. The small-time li
mit highlights how infinitely many singularities a
re born at $t = 0$ and how they orientate themselv
es to lie increasingly close to anti-Stokes lines
in the far-field of the inner problem. This inner
problem also reveals whether or not the closest si
ngularity to the real axis moves toward the axis o
r away. Further analysis characterises the motion
of the singularities for intermediate and late tim
es. While Burgers&rsquo\; equation has an exact so
lution\, we deliberately apply a mix of techniques
in our analysis in an attempt to develop methodol
ogy that can be applied to other nonlinear partial
differential equations that do not.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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