We study the propagation of singularities for semilinear Schroedinger 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.
Propagation of Gabor singularities for semilinear Schroedinger equations
RODINO, Luigi Giacomo
2015-01-01
Abstract
We study the propagation of singularities for semilinear Schroedinger 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.
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