Propagation of singularities for anharmonic Schr\"odinger equations

TL;DR

This paper studies how singularities propagate in solutions to certain anharmonic Schrödinger equations, establishing well-posedness in specialized function spaces and analyzing singularity behavior.

Contribution

It introduces a framework for analyzing singularity propagation in anharmonic Schrödinger equations within anisotropic Shubin--Sobolev modulation spaces.

Findings

Well-posedness of the Cauchy problem in specific function spaces

Propagation properties of singularities in solutions

Extension of analysis to generalized anharmonic oscillators

Abstract

We consider evolution equations for two classes of generalized anharmonic oscillators and the associated initial value problem in the space of tempered distributions. We prove that the Cauchy problem is well posed in anisotropic Shubin--Sobolev modulation spaces of Hilbert type, and we investigate propagation of suitable notions of singularities.