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SUMMARY:Numerical spectral synthesis of soliton and breather gas - Giacomo
  Roberti (Northumbria University)
DTSTART:20220818T100000Z
DTEND:20220818T103000Z
UID:TALK177422@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\, &nbsp\;we present the algorithms for the synthesis 
 of soliton and breather gases in the KdV and fNLS framework and we discuss
  the theoretical and numerical challenges that arise in the implementation
 . This is joint work with P. Suret\, S. Randoux\, G. El and T. Congy.
LOCATION:Seminar Room 2\, Newton Institute
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