Simultaneous diffusion and reaction processes in plasma dynamics

A particular solution, which describes the shape-preserving evolution of an explosive localized state (ELS) in one, two, and three spatial dimensions, is obtained for the reaction-diffusion equation with a quadratic creative reaction term. This state, the ELS, is discovered to be of fundamental significance, since states which are ``nearby'' an ELS are attracted to it. A new technique of analysis is introduced, which enables one to describe the dynamical evolution of the amplitude and width of density profiles. These variables are found to be governed by two coupled nonlinear differential equations. The dynamic theory covers, in a unified form, the cases of one, two, and three spatial dimensions.