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

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 (IST). A key ingredient in the analysis is the L2{L}^{2}-Sobolev bijectivity of the direct and IST established by Xin Zhou for the focusing Zakharov-Shabat problem.

Keywords

• maxwell-bloch equations
• well-posedness
• integrable systems
• inverse scattering transform
• inhomogeneous broadening
• 35q55
• 35q58
• 35a05
• 37k15