Wave front set for solutions to Schrodinger equations with time-dependent variable coefficients

TL;DR

This paper characterizes the smoothness and singularity structure of solutions to Schrödinger equations with time-dependent coefficients using wave front sets and wave packet transforms, extending previous methods.

Contribution

It introduces a novel approach to analyze wave front sets of Schrödinger solutions with variable coefficients, surpassing the limitations of Kato-Ito methods.

Findings

Wave front sets of solutions are characterized using wave packet transforms.

The method handles time-dependent coefficients and potentials effectively.

Perturbation terms are estimated with new techniques.

Abstract

In this paper, we determine the C-infinity type wave front sets of the solutions to the Schrodinger equations with time-dependent variable coefficients and potentials by using the wave packet transform. We introduce the infinite sum and estimate the perturb terms of the flat Laplacian on flat plane, which cannot be estimated by the method in Kato-Ito.