  In this paper we deal with the well-known nonlinear Lorenz system that
describes the deterministic chaos phenomenon. We consider an interesting
problem with time-varying phenomena in quantum optics. Then we establish from
the motion equations the passage to the Lorenz system. Furthermore, we show
that the reduction to the third order non linear equation can be performed.
Therefore, the obtained differential equation can be analytically solved in
some special cases and transformed to Abel, Dufing, Painlev\'{e} and
generalized Emden-Fowler equations. So, a motivating technique that permitted a
complete and partial integrability of the Lorenz system is presented.
