The nonlinear dynamics of wave systems with spatio-temporal collapses

Wave energy concentration processes in nonlinear media are analysed. A classification of nonlinear systems with wave collapses according to the character of the field energy localization into singularity domains is presented, and examples of the evolution are considered. A detailed analysis is given for the case of the bievolutional (spatio-temporal) behavior of strong electromagnetic waves in media with nonlinearity inertia where an arbitrary energy flux can be trapped into contracting filaments, or moving focus distributions. (orig.)