WAVE COLLAPSE IN PHYSICS - PRINCIPLES AND APPLICATIONS TO LIGHT AND PLASMA-WAVES

The collapse of self-focusing waves described by the nonlinear Schrodi nger (NLS) equation and the Zakharov equations in nonlinear optics and plasma turbulence is reviewed. Special attention is paid to the blow- up properties of solutions to the NLS equation with a power nonlineari ty. Conditions for blow-up and global existence of these solutions, to gether with criteria for the stability of stationary waves are recalle d. The variational approach, the so-called exactly and quasi- self-sim ilar analyses employed for modelling wave collapse are then compared. Besides, the influence of the group-velocity dispersion and deviations from the spatio-temporal envelope approximations are investigated as structural perturbations of the NLS standard models, which can strongl y alter the blow-up dynamics. Finally, a detailed description of wave collapses in materials with quadratic and cubic responses and a map-ma king of the interaction regimes between two light cells in Kerr media complete this review. (C) 1998 Elsevier Science B.V. All rights reserv ed.