Spectral limits for periodic pattern propagation in Kerr media

We consider the propagation of periodic waves with initially narrow spatial spectra in a Kerr medium. The set of constants of motion closely related to the order amplitudes is introduced. It is shown that the spatial spectrum remains uniformly narrow with propagation for both self-focusing and self-defocusing nonlinearity. In addition, for sufficiently weak nonlinearity, initially strong orders always remain strong. Thus the problem is shown to be essentially finite dimensional and well approximated by a proper set of coupled ordinary differential equations. (C) 2004 Optical Society of America.