On the Cauchy problem for some systems occurring in nonlinear optics

Abstract

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.