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SUMMARY:The theory of periodic anomalous (rogue) waves in continuous and d
 iscrete NLS type equations
DTSTART;VALUE=DATE-TIME:20230621T071500Z
DTEND;VALUE=DATE-TIME:20230621T074500Z
DTSTAMP;VALUE=DATE-TIME:20260517T162357Z
UID:indico-contribution-64@cern.ch
DESCRIPTION:Speakers: Prof. SANTINI\, Paolo (University of Roma "La Sapien
 za")\nModulation instability and nonlinearity are the main causes of the a
 ppearance of anomalous (rogue) waves (AWs) in several physical contexts. T
 he theory of periodic anomalous waves has been recently developed on the b
 asic Nonlinear Schrödinger (NLS) model in 1+1 dimensions\, adapting the f
 inite gap method to the Cauchy problem for periodic initial perturbations 
 of the homogeneous background solution of NLS [1]. This theory allows one 
 to express the solution of the Cauchy problem\, to leading order\, in term
 s of elementary functions of the unstable part of the initial data\, and h
 as already been tested in the nonlinear optics of a photorefractive crysta
 l [2]. Also a perturbation theory of AWs allowing one to study the leading
  order effects of small perturbations of the NLS equation on the dynamics 
 of AWs has been constructed [3]. In this lecture we develop a lattice theo
 ry of AWs using as basic model the Ablowitz-Ladik lattice\, integrable dis
 cretization of the NLS equation [4]\, [5].\n\n[1] P. G. Grinevich and P. M
 . Santini: ``The finite-gap method and the periodic NLS Cauchy problem of 
 anomalous waves for a finite number of unstable modes''\, Russian Math. Su
 rveys {\\bf 74:2} 211-263 (2019). DOI:10.1070/RM9863.\n[2] D. Pierangeli\,
  M. Flammini\, L. Zhang\, G. Marcucci\, A. J. Agranat\, P. G. Grinevich\, 
 P. M. Santini\, C. Conti\, and E. DelRe\, ``Observation of exact Fermi-Pas
 ta-Ulam-Tsingou recurrence and its exact dynamics''\, Phys. Rev. X {\\bf 8
 }\, 041017 (2018). doi.org/10.1103/ PhysRevX.8.041017. \n[3] F. Coppini\, 
 P. G. Grinevich and P. M. Santini: ``The effect of a small loss or gain in
  the periodic NLS anomalous wave dynamics. I''\,  Phys. Rev. E {\\bf 101}\
 , 032204 (2020). DOI: 10.1103/PhysRevE.101.032204. arXiv:1910.13176. \n[4]
  F. Coppini and P. M. Santini: ``Modulation instability\, periodic anomalo
 us wave recurrence\, and blow up in the Ablowitz - Ladik lattices''. Prepr
 int 2023. \n[5] F. Coppini and P. M. Santini: ``The effect of loss/gain an
 d hamiltonian perturbations of the Ablowitz - Ladik lattice on the recurre
 nce of periodic anomalous waves''. Preprint 2023.\n\nhttp://indico.fuw.edu
 .pl/contributionDisplay.py?contribId=64&sessionId=5&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=64&sessionId
 =5&confId=67
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