On the Cauchy problem for some systems occurring in nonlinear optics

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 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 Maxwell-Bloch system.

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Advances in Differential Equations, 3, 473–496 (1998)