We investigate the propagation of periodic patterns in one and two dimensions for weak Kerr-type nonlinearity. Nonlinear amplitudes are introduced, which are related to the Fourier harmonics of a wave by polynomials of third and fifth degree. These amplitudes evolve in a particularly simple way and permit easy reconstruction of waveform after propagation. For the one-dimensional case, solutions are quasiperiodic, and solitonlike structures can be identified. For the two-dimensional case, recurrent and chaotic regimes exist depending on lattice type.