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arXiv · 2407.19770

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

Gino Biondini·Barbara Prinari·Zechuan Zhang
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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.

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Gino Biondini, Barbara Prinari, Zechuan Zhang. 2024-07-29. Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening. https://arxiv.org/abs/2407.19770

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