MODULATIONAL INSTABILITY DYNAMICS IN A SPATIAL FOCUSING AND TEMPORAL DEFOCUSING MEDIUM

The modulational instability of a wave in media where the nonlinearity has a focusing-in-space and defocusing-in-time character is investiga ted. An approximate self-similar solution of the nonlinear Schrodinger equation is derived for this nonlinearity and is used as background e nvelope of the wave. We show that this background wave envelope can in itially enhance exponential growth of a transverse spatial modulation. The analysis is extended to the case of a modulation in both time and space, and it is found that such a spatiotemporal modulation can be u nstable as well.