Propagation of 3d optical buillets in quadratically nonlinear media

Three-dimensional light beams-pulses, known as light bullets, are studied analytically and numerically. Using the method of the averaged Lagrangian obtained analytical solution describing a bullet in nonlinear parametric interaction. The obtained conditions for sustainable spread of bullets, which is a ratio between diffraction, dispersion and nonlinear lengths. Analytical conclusions are confirmed in the process of computer simulation. The calculations demonstrate that the light bullet extends to a distance far exceeding the dispersion and diffraction lengths in the anisotropic medium. Separately the cases of stable propagation of two-component three-dimensional light bullets, as well as the formation of the beam pulse by generating the second optical harmonic.