The authors consider the propagation of a thermonuclear burn in a plasma with a density profile rho varies as 1/r. Using direct numerical simulation of the burn in a DT plasma, taking into account, in particular, alpha transport, heat conduction and different electron and ion temperatures, it is shown that in the spherically symmetric case the burn is self-similar for β > β_cr = 0.43 g/cm². The possibility is discussed of prolonged propagation of a self-similar burn along the cone of the Z pinch neck, in which the necessary density profiling can occur naturally through compression dynamics