  We present an analytical approach to the theory of nonlinear propagation of
femtosecond optical pulses with broad-band spectrum in gases. The vector
character of the nonlinear third-order polarization is investigated in details,
taking into account the carrier to envelope phase. The corresponding system of
vector amplitude equations is written by using left-hand and right-hand
circular components of the electrical field. We found that this system
nonlinear equations admits $3D+1$ vector soliton solution with Lorentz shape.
The solution presents relatively stable propagation and rotation with GHz
frequency of the vector of the electrical field in plane, orthogonal to the
direction of propagation. The evolution of the intensity profile demonstrate
weak self-compression and week spherical wave in the first milliseconds of
propagation.
