Numerical solution of the Maxwell equations in nonlinear media

In this paper some aspects concerning the finite element solution of the electromagnetic propagation in nonlinear media are studied through complementary formulations of the Maxwell equations. Nonlinear hyperbolic equations generate discontinuous solutions even if the initial and boundary conditions are regular. The numerical solution definitively breaks and the Galerkin method does not converge any more after the time at which a sharp discontinuity is developed. The sharpening of the solution is related to the loss of its uniqueness.