Solutions which approximately describe the effect of strong thermal self-ac
tion of a laser beam in weakly absorbing media (gases and liquids) have bee
n obtained. This paper considers the regimes of thermal conductivity, trans
verse flows of gases at subsonic and supersonic velocities, transonic nonli
near regime, and gravitational convection in a horizontal beam. Assuming th
at the shape of transverse intensity distribution is constant, and that the
wave front can be approximated by a second-power polynomial, ordinary diff
erential equations and their solutions for average transverse dimensions of
beams have been obtained. These approximate solutions are in satisfactory
agreement with exact solutions. (C) 1999 American Institute of Physics. [S1
063-7761(99)01007-0].