Generation of a train of three-dimensional optical solitons in a self-focusing medium

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Abstract
The problem of modulation instability of a self-focused beam in a homogeneous nonlinear medium with saturation and anomalous group-velocity dispersion is solved numerically. It is shown that the results of this instability is beam breakup into a periodic train of three-dimensional (3D) spatial solitary waves. It is also shown that other types of periodic initial conditions can produce a periodic train of 3D spatial solitary waves. Our numerical simulations show that 3D solitary waves are attractors (foci or limit cycles) in the Hilbert space of solutions of the 3D nonlinear Schrödinger equation. A field of another configuration can converge to them upon propagation and after the emission of a certain amount of radiation.