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Propagation of Gabor singularities for semilinear Schrödinger equations

  • Fabio NicolaEmail author
  • Luigi Rodino
Article

Abstract

We study the propagation of singularities for semilinear Schrödinger equations with quadratic Hamiltonians, in particular for the semilinear harmonic oscillator. We show that the propagation still occurs along the flow of the Hamiltonian field, but for Sobolev regularities in a certain range, in terms of a suitable definition of the global Sobolev-wave front set.

Keywords

Time-frequency analysis Schrödinger equations Global wave front set Propagation of singularities 

Mathematics Subject Classification

35Q55 35A21 35S05 35S50 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Dipartimento di Scienze MatematichePolitecnico di TorinoTurinItaly
  2. 2.Dipartimento di MatematicaUniversità di TorinoTurinItaly

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