Intermediate Models in Nonlinear Optics

In this paper, new models are derived for laser propagation in a nonlinear medium. These models are intermediate between nonlinear Maxwell systems and nonlinear Schrödinger equations and are exact in linear cases. We prove rigorous error estimates for a generic class of systems. In the last section, we perform numerical tests in order to investigate the numerical effectivity of the bounds given by the theorem. We compare for a particular nonlinear system the exact solutions and the approximate solutions given by our new model. It is shown that the new models behave as predicted by the theorem but are even better in some cases.