THE INTERACTION REPRESENTATION IN THE SELF-FOCUSING THEORY

The general scheme of dividing the solution of the nonlinear Schrodinger equation (2D case) into the focused (singular) part of the beam called the "peak" and the rest (nonsingular) part, the "background", is presented. The peak is compared with a manifold of self-similar modes whose dynamics is analysed. It is shown that if the beam power is less than critical, the self-similar beam is strictly localized. If the beam power is more than critical the self-similar solution is a quasi-localized mode with tunnel emission of power from the paraxial region and the width of the peak tends to zero. The parametric peak-background interaction analysis proves that the limiting self-focusing law a(t) approximately [(t0 - t)/ln\ln(t0 - t)\]1/2 is determined only by the peak dynamics.