Modified Scattering for the Schr\"odinger-Bopp-Podolsky Equation

TL;DR

This paper establishes sharp decay rates and modified scattering behavior for solutions to the Schr"odinger-Bopp-Podolsky equation in two and three dimensions, given small initial data in a weighted Sobolev space.

Contribution

It provides the first rigorous proof of sharp decay and modified scattering for the Schr"odinger-Bopp-Podolsky equation in low dimensions.

Findings

Proved sharp $L^ abla$ decay rates for solutions.

Established modified scattering behavior in 2D and 3D.

Demonstrated results for small initial data in weighted Sobolev spaces.

Abstract

We prove sharp $L^\infty$ decay and modified scattering for the Schr\"odinger-Bopp-Podolsky equation in $2$ and $3$ spatial dimensions with small initial data chosen from a weighted Sobolev space.