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SUMMARY:Numerical spectral synthesis of soliton and breather gases - Giaco
 mo Roberti (Northumbria University)
DTSTART:20221020T153000Z
DTEND:20221020T160000Z
UID:TALK182597@talks.cam.ac.uk
DESCRIPTION:Soliton gas was introduced by Zakharov [Sov. Phys. JETP 33\, 5
 38 (1971)] as an infinite ensemble of interacting KdV solitons randomly di
 stributed in velocity and positions. This concept has been extended by El 
 and Tovbis [PRE\, 101\, 052207 (2020)]\, in their development of the spect
 ral theory of soliton and breather gases\, in the framework of the focusin
 g Nonlinear Schrodinger (fNLS) equation. Moreover\, it has been shown in a
  recent work by Gelash et al. [PRL\, 123\, 234102 (2019)] how the spectral
  soliton gas formalism could lead to a new understanding of the evolution 
 of random processes in integrable systems\, the so-called integrable turbu
 lence.\nIn this context\, the ability to numerically build the soliton and
  breather gas solutions from the nonlinear spectral plane is a key element
  for testing the mathematical model and investigating its physical applica
 tions.\nIn this work\, we present the algorithms for the synthesis of soli
 ton and breather gases in the KdV and fNLS framework and we discuss the th
 eoretical and numerical challenges that arise in the implementation.\n&nbs
 p\;\nThis is joint work with A. Tovbis\, P. Suret\, S. Randoux\, G. El and
  T. Congy.
LOCATION:Seminar Room 1\, Newton Institute
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