Non-linear dynamics and geometrical properties of localized wave structures

The present state of investigations of geometric properties of spatially localized configurations of electromagnetic wave fields with TE and TM polarizations is reviewed. The spatial structures of these field configurations are determined by their discrete amplitude spectra. The possibilities of controlled formation of localized field structure with different symmetries are analysed. The non-linear dynamics of such distributions, depending upon their initial geometric properties, are considered for series of realistic models of non-linear media. The utilization of adequate analytical methods, including a geometric analysis in special space, a generalized variational approach, an inverse scattering method for non-stationary processes, is illustrated. The new tendencies in non-linear dynamics of short polarized signals in directional systems are outlined.