Solutions of a generalized Emden equation and their physical significance

A generalized Emden equation is shown to appear in the description of a wide variety of critical systems as a reduced equation for multidimensional kinetic equations for the order parameter. We have surveyed some of the known solutions and found a number of types of physical behavior such as singular, decaying, and oscillatory damped. A new method of finding appropriate solutions has been given together with, in some cases, severe restrictions on its use. An important link between a generalized Emden equation and an autonomous equation for a damped anharmonic oscillator has been found and exploited.