In this paper, self-focusing of finite Airy–Gaussian (AiG) laser beams in collisionless plasma has been investigated. The source of nonlinearity considered herein is relativistic. Based on the Wentzel–Kramers–Brillouin (WKB) and paraxial-ray approximations, the nonlinear coupled differential equations for beam-width parameters in transverse dimensions of AiG beams have been established. The effect of beam's modulation parameter and linear absorption coefficient on the self-focusing/defocusing of the beams is specifically considered. It is found that self-focusing/defocusing of finite AiG beams depends on the range of modulation parameter. The extent of self-focusing is found to decrease with increase in absorption.
