Stabilizing effects of dispersion management

A cubic nonlinear Schrodinger equation (NLS) with periodically varying disp ersion coefficient, as it arises in the context of fiber-optics communicati on, is considered. For sufficiently strong variation, corresponding to the so-called strong dispersion management regime, the equation possesses pulse -like solutions which evolve nearly periodically. This phenomenon is explai ned by constructing ground states for the averaged variational principle an d justifying the averaging procedure. Furthermore, it is shown that in cert ain critical cases (e.g. quintic nonlinearity in one dimension and cubic no nlinearity in two dimensions) the dispersion management technique stabilize s the pulses which otherwise would be unstable. This observation seems to b e new and is reminiscent of the well-known Kapitza's effect of stabilizing the inverted pendulum by rapidly moving its pivot. (C) 2001 Published by El sevier Science B.V.