In this paper, the propagation of an intense laser beam in a collisional plasma channel is studied analytically, and the investigation is focused on the self-focusing due to the Kerr nonlinearity, the relativistic nonlinearity, and the electron density perturbation. The propagation of laser, including the effects of diffraction, the plasma channel, the 3rd Kerr nonlinearity, the relativistic self-focusing, the electron density perturbation, land the defocusing due to electron collisions, is analyzed. The source-dependent expansion (SDE) method for analyzing the wave equation is introduced and employed in the paper.