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

Gino Biondini; Barbara Prinari; Zechuan Zhang

doi:10.1515/anona-2024-0054

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

Gino Biondini
, Barbara Prinari
, Zechuan Zhang

Mathematics

SUNY Buffalo

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 L 2 -Sobolev bijectivity of the direct and IST established by Xin Zhou for the focusing Zakharov-Shabat problem.

Original language	English
Article number	20240054
Journal	Advances in Nonlinear Analysis
Volume	13
Issue number	1
DOIs	https://doi.org/10.1515/anona-2024-0054
State	Published - Jan 1 2024

Keywords

Maxwell-Bloch equations
inhomogeneous broadening
integrable systems
inverse scattering transform
well-posedness

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

keywords = "Maxwell-Bloch equations, inhomogeneous broadening, integrable systems, inverse scattering transform, well-posedness",

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AU - Biondini, Gino

AU - Prinari, Barbara

AU - Zhang, Zechuan

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Y1 - 2024/1/1

N2 - 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 L 2 -Sobolev bijectivity of the direct and IST established by Xin Zhou for the focusing Zakharov-Shabat problem.

AB - 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 L 2 -Sobolev bijectivity of the direct and IST established by Xin Zhou for the focusing Zakharov-Shabat problem.

KW - Maxwell-Bloch equations

KW - inhomogeneous broadening

KW - integrable systems

KW - inverse scattering transform

KW - well-posedness

UR - https://www.scopus.com/pages/publications/85213036860

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DO - 10.1515/anona-2024-0054

M3 - Article

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VL - 13

JO - Advances in Nonlinear Analysis

JF - Advances in Nonlinear Analysis

IS - 1

M1 - 20240054

ER -

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

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Keywords

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