this book presents an up-to-date review of methods for constructing a specific class of asymptotic solutions, called self-stabilizing solutions. this class includes solitons, kinks, travelling waves, etc. either the solutions for this class or their derivatives are localized in the neighbourhood of a certain curve of surface. the book can be divided into two parts: chapters i-v contain the methods for constructing asymptotic solutions, and in chapters vi-vii these are applied to some concrete problems. the appendix briefly discusses a method for the justification of some asymptotic solutions. audience: this book will be of interest to specialists both in differential equations and in the mathematical modelling of physical and chemical processes.