Qualitative theory of stable stationary localized structures in one dimension

Abstract

In this paper we study the existence, the stability properties, and the bifurcation structure of static localized solutions in one dimension, near the robust existence of stable fronts between homogeneous solutions and periodic patterns. We use the qualitative theory of differential equation to reinterpret the theory of these stable fronts as developed by Pomeau, and then use the same framework to develop a theory of stationary localized structures.