scholarly journals Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials

2015 ◽  
Vol 27 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Elena Cordero ◽  
Fabio Nicola ◽  
Luigi Rodino
Keyword(s):  
Wave Front ◽  
Modulation Spaces ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Wave Front Set ◽  
Local Propagation ◽  
The Cauchy Problem ◽  
Wave Front Sets ◽  
Propagation Of Singularities ◽  
Gabor Wave Front Set

We consider Schrödinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may not even be differentiable. The well-posedness of the Cauchy problem is proved in the frame of the modulation spaces, and results of micro-local propagation of singularities are given in terms of Gabor wave front sets.

scholarly journals Precise propagation of singularities for a hyperbolic system with characteristics of variable multiplicity

1986 ◽  
Vol 101 ◽  
pp. 111-130 ◽  
Author(s):  
Chisato Iwasaki ◽  
Yoshinori Morimoto
Keyword(s):  
Cauchy Problem ◽  
Wave Front ◽  
Hyperbolic System ◽  
Wave Front Set ◽  
Variable Multiplicity ◽  
The Cauchy Problem ◽  
Propagation Of Singularities ◽  
Admissible Trajectory

In this paper we consider the Cauchy problem for a hyperbolic system with characteristics of variable multiplicity and construct a certain solution whose wave front set propagates precisely along the so-called “broken null bicharacteristic flow”, in other words, along the admissible trajectory if we use the terminology of [6].

scholarly journals Analytic wave front set for solutions to Schrödinger equations

2009 ◽  
Vol 222 (4) ◽  
pp. 1277-1307 ◽  
Author(s):  
André Martinez ◽  
Shu Nakamura ◽  
Vania Sordoni
Keyword(s):  
Wave Front ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Wave Front Set ◽  
Analytic Wave
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