  The effects of the non-linearity of the medium on the growth rate of
filamentation instability in a magnetized plasma interacting with an intense
laser pulse, is investigated. The non-linearity of the medium, modeled by Kerr
non-linearity, is an important factor, which determines the rate of instability
growth. Sensitivity of the rate of filamentation growth, to the Kerr non-linear
coefficient could be adjusted by the external magnetic field and laser
intensity.
