On the structure of self-compressing blobs of an electromagnetic field in dispersive media with cubic nonlinearity

Abstract

We obtained an asymptotic solution of the nonlinear Schrödinger equation with dimension (3+1) that describes the behavior of an electromagnetic field near the singularity arising in the case of propagation of electromagnetic waves in a dispersive medium with cubic nonlinearity as a result of development of the modulation-self-focusing instability. According to the developed theory, there exists a finite volume of the medium occupied by the electromagnetic field in which the energy flux is directed toward the emerging singularity. The energy contained in this volume, which is the characteristic parameter of instability, turns out to be a finite value depending on the parameters of the medium and the value of the field against the background of which the singularity takes place. The above energy is much smaller than the energy per characteristic scale of the most rapidly increasing unstable perturbations of the field with uniform amplitude distribution. In the conclusion, we discuss the possibility of using the collapse phenomenon for the formation of electromagnetic-field pulses.