Theoretical analysis demonstrates local and global well-posedness in Maxwell-Bloch systems, suggesting rigorous solvability via inverse scattering transforms.
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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>L</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> {L}² -Sobolev bijectivity of the direct and IST established by Xin Zhou for the focusing Zakharov-Shabat problem.
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Biondini et al. (2024) studied this question.
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