Numerical Approximation of Kerr-debye Equations

We investigate finite volume schemes for the one-dimensional Kerr-Debye model of electromagnetic propagation in nonlinear media. In this relaxation quasilinear hyperbolic system, the relaxation parameter is the response time of the media. When it tends to zero, the relaxed limit is known as the Kerr system. We show that basic explicit splitting methods fail to preserve this asymptotic. Following two different viewpoints, we construct splitting implicit and well-balanced explicit approximations which are stable, entropic and own the correct asymptotic behavior. Various numerical experiments are performed.