Advances in Differential Equations

On the Cauchy problem for some systems occurring in nonlinear optics

Brigitte Bidégaray

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We study the Cauchy problem for two systems of equations (Maxwell--Debye and Maxwell--Bloch) describing laser-matter interaction phenomena. We show that these problems are locally-in-time well-posed for initial data in different Sobolev spaces. In the case of the Maxwell--Debye system, which contains some delay term, we study the limit of the solutions when this delay tends to 0. We also consider an adiabatic approximation of the Maxwell--Bloch system.

Article information

Adv. Differential Equations, Volume 3, Number 3 (1998), 473-496.

First available in Project Euclid: 19 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 78A60: Lasers, masers, optical bistability, nonlinear optics [See also 81V80]
Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory 78A10: Physical optics


Bidégaray, Brigitte. On the Cauchy problem for some systems occurring in nonlinear optics. Adv. Differential Equations 3 (1998), no. 3, 473--496.

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