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SUMMARY:Soliton versus the gas: Fredholm determinants\, analysis\, and kin
 etic equations - Manuela Girotti (Saint Mary's University)
DTSTART:20220906T093000Z
DTEND:20220906T103000Z
UID:TALK177833@talks.cam.ac.uk
DESCRIPTION:We analyze the case of a dense mKdV soliton gas and its large 
 time behaviour in the presence of a single 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 the sum of the background gas solution (a modulated ellipti
 c wave)\, plus a soliton solution: the individual expressions are however 
 quite convoluted due to the interaction dynamics. Additionally\, we are ab
 le to derive the local phase shift of the gas after the passage of the sol
 iton\, and we can trace the location of the soliton peak as the dynamics e
 volves. Finally we show that the soliton peak\, while interacting with the
  soliton gas\, has an oscillatory velocity whose leading order average val
 ue satisfies the kinetic velocity equation analogous to the one posited by
  V. Zakharov and G. El.
LOCATION:Seminar Room 1\, Newton Institute
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