Coupled-mode versus nonlinear Schrodinger equations for electromagnetic wave propagation in continuous media

We investigate Electromagnetic-Wave propagation in continuous media in which the presence of nonlinearities gives rise to parametric mixing. The case of a laser pulse injected in an optical fiber has been analyzed. This propagation is described by means of the Nonlinear Schrodinger Equation (NLS). On one side, we integrate numerically the NLS with different injection conditions describing phase and amplitude modulation as well as wave mixing phenomena. On the other side we illustrate a simplified model of coupled-mode equations giving an Hamiltonian description of the problem which enable us to obtain analytical solutions. We compare and discuss the results obtained with the two different approaches relatively to the same input conditions.