The Non-Linear Geometric Optics of the Localized Wave Fields

The new approach to the self-action theory of intensive localized pulses, based on the hydrodynamical analogy in the non-linear geometrical optics, is proposed. The complex of phenomena of amplitude-phase non-stationary evolution of the intensive localized electromagnetic wave pulses in the dispersive medium is analysed in the framework of such approach. The wide classes of exact analytical solutions of the non-linear self-action equations, connected with such pulses, are constructed. The simple form of these solutions, represented with the well-known eigen-functions of the Laplace equation in special variables, permits to divide the pulse non-linear deformation qualitatively different effects. These solutions predict the large-scale pulse self-stratification and the origin of the quick intensity increase area during the non-linear evolution of the initially smooth distribution of the wave. The characteristic points of such evolution are represented by the singularities in the exact solutions of the non-linear geometrical optics. All results, describing the dynamics of the non-linear amplitude-phase re-building of the pulse, are represented in the simple algebraic form.