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Fumihito Abe

Publications and source records attributed to Fumihito Abe.

2 recordsLinked to original sources
arXiv2026

Wave front set of solutions to Schr\"{o}dinger equations with time-dependent magnetic fields

In this paper, we determine the wave front set of solutions to the Schr\"{o}dinger equation with time-dependent magnetic fields. We considered time-dependent and `not so small' magnetic fields through the method using the wave packet transform established by K. Kato, M. Kobayashi and S. Ito. Furthermore, we checked that the fundamental solution of the Schr\"odinger equation in a spatially decaying magnetic field has no singularities as a consequence of our result.

math.AP↗
arXiv2024

Singularities of solutions to nonlinear Schrödinger equations

We study the wave front set of the solutions of the initial value problem for nonlinear Schrödinger equations via wave packet transform. We give an sufficient condition which assures that the solutions is in Sobolev space of order s in a given direction at a given time.

math.AP↗