Analysis of a Galerkin approach applied to a system of coupled Schrödinger equations

We study error and convergence rate of a fully discrete Fourier-Galerkin scheme to approximate the solutions of a system consisting of two coupled cubic Schrödinger equations with cross modulation, which is a model for the propagation of a nonlinear pulse in a linearly birefringent Kerr optical fiber. We also establish a result on existence and uniqueness of a solution of the corresponding initial value problem.