Explosive Evolution of Self-Preserving Local Structures

摘要

It has recently been noticed that certain forms of localized structures can grow explosively in time without change in spatial structure. Explicit forms, which describe their evolution are obtained as solutions of reaction-diffusion equations. It is the purpose of the present investigation to analyze the influence of perturbations on such solutions. The analysis will be generalized to consider the interaction of three variables, e.g. a three-wave system, as described by three coupled reaction-diffusion equations. Equilibria, i.e. time-independent solutions corresponding to the explosive-type reaction-diffusion equations, are also determined and their properties of stability are analyzed. (ERA citation 13:055864)