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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Soliton versus the gas: Fredholm determinants\, an
alysis\, and kinetic equations - Manuela Girotti (
Saint Mary's University)
DTSTART;TZID=Europe/London:20220906T103000
DTEND;TZID=Europe/London:20220906T113000
UID:TALK177833AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/177833
DESCRIPTION:We analyze the case of a dense mKdV soliton gas an
d its large time behaviour in the presence of a si
ngle trial soliton. We show that the solution can
be expressed in terms of Fredholm determinants as
well as in terms of a Riemann-Hilbert problem. We
then show that the solution can be decomposed as t
he sum of the background gas solution (a modulated
elliptic wave)\, plus a soliton solution: the ind
ividual expressions are however quite convoluted d
ue to the interaction dynamics. Additionally\, we
are able to derive the local phase shift of the ga
s after the passage of the soliton\, and we can tr
ace the location of the soliton peak as the dynami
cs evolves. Finally we show that the soliton peak\
, while interacting with the soliton gas\, has an
oscillatory velocity whose leading order average v
alue satisfies the kinetic velocity equation analo
gous to the one posited by V. Zakharov and G. El.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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