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CATEGORIES:Academics,Lectures & conferences
DESCRIPTION:Please join us remotely for a seminar by FIU graduate student A
lex David Rodriquez.\n\nRodriguez considers the one-dimensional nonlinear S
chrödinger equation iut + uxx + N (u) = 0\, x\, t R\, with the nonlinearit
y term that is expressed as a sum of powers\, possibly infinite: N (u) = Xc
n|u| n u\, n > 0. The combined nonlinearities appear in various physical ap
plications such as chemical super fluidity\, or the description of elementa
ry particles such as bosons and defectons\, or other subatomic structures\,
and in approximations of anisotropic media. We first investigate the local
well-posedness of this equation for any positive powers of in a certain w
eighted class of initial data\, subset of H1 (R). Then\, using the pseudoco
nformal transformation\, we extend the local result to the global well-pose
dness. Furthermore\, we investigate the asymptotic behavior of global solut
ions\, those that have initial data with a quadratic phase e ib|x| 2 with s
ufficiently large positive b\, in particular\, we prove scattering of these
solutions in H1 (R). One of the advantages of considering an infinite sum
in the nonlinear term is the investigation of an exponential nonlinearity e
|u|u and its well-posedness in that case\, the first such result. To concl
ude\, we show numerical simulations in the focusing case for various cases
of combined nonlinearities\, including the exponential one\, and investigat
e a threshold behavior for the global versus finite time existing solutions
\, which extends our theoretical results. This talk is based on the joint w
ork with Gia Azcotia\, Oscar Riano\, Svetlana Roudenko and Hannah Wubben\,
which was initiated during the Research Experiences for Undergraduates prog
ram “AMRPU @ FIU” in Summer 2021.\n\nHosted by Hakima Bessiah.
DTEND:20220225T220000Z
DTSTAMP:20220817T142319Z
DTSTART:20220225T210000Z
LOCATION:
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SUMMARY:Applied Math Seminar: The NLS with Combined Nonlinearities by FIU G
raduate Student Alex David Rodriguez
UID:tag:localist.com\,2008:EventInstance_39176977983347
URL:https://calendar.fiu.edu/event/applied_math_seminar_by_graduate_student
_alex_rodriguez
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