Theoretical investigation on nonlinear propagation characteristics of \(q\) -Gaussian laser beams propagating through preformed collisional plasma channels has been presented. Following a semi analytical technique known as moment method, an approximate solution of nonlinear wave equation governing the evolution of beam envelope has been obtained. Particularly the phenomena of self-focusing and self-phase modulation have been investigated in detail. The effect of deviation of beam profile from ideal Gaussian profile, occurring as a consequence of cavity imperfections, has been incorporated through Tsalli's \(q\) -Gaussian distribution.
