Numerical aspects of nonlinear Schrödinger equations in the presence of caustics (Articolo in rivista)

Type
Label
  • Numerical aspects of nonlinear Schrödinger equations in the presence of caustics (Articolo in rivista) (literal)
Anno
  • 2007-01-01T00:00:00+01:00 (literal)
Alternative label
  • Carles R., Gosse L. (2007)
    Numerical aspects of nonlinear Schrödinger equations in the presence of caustics
    in Mathematical models and methods in applied sciences
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Carles R., Gosse L. (literal)
Pagina inizio
  • 1531 (literal)
Pagina fine
  • 1553 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 17 (literal)
Rivista
Note
  • ISI Web of Science (WOS) (literal)
Titolo
  • Numerical aspects of nonlinear Schrödinger equations in the presence of caustics (literal)
Abstract
  • The aim of this text is to develop on the asymptotics of some 1-D nonlinear Schr\"odinger equations from both the theoretical and the numerical perspectives, when a caustic is formed. We review rigorous results in the field and give some heuristics in cases where justification is still needed. The scattering operator theory is recalled. Numerical experiments are carried out on the focus point singularity for which several results have been proven rigorously. Furthermore, the scattering operator is numerically studied. Finally, experiments on the cusp caustic are displayed, and similarities with the focus point are discussed. Several shortcomings of spectral time-splitting schemes are investigated. (literal)
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