Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening

TL;DR

This paper proves local and global well-posedness for the Maxwell-Bloch equations with inhomogeneous broadening using inverse scattering transform techniques, leveraging integrability properties of the system.

Contribution

It establishes well-posedness results for the Maxwell-Bloch system with inhomogeneous broadening via inverse scattering, a novel application of integrability methods.

Findings

Proved local and global well-posedness of the system.

Utilized inverse scattering transform and integrability properties.

Connected the analysis to the focusing Zakharov-Shabat problem.

Abstract

The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making use of the corresponding inverse scattering transform. A key ingredient in the analysis is the $L^2$-Sobolev bijectivity of the direct and inverse scattering transform established by Xin Zhou for the focusing Zakharov-Shabat problem.