Construction of uniform asymptotic solutions of wave-type differential equations by methods of catastrophe theory

Abstract

A mathematical apparatus for solving differential equations of special type by the methods of main, edge, and corner catastrophes is developed. The fundamentals of the wave catastrophe theory are considered, including the classification and methods of constructing uniform asymptotics used to describe the structure of wave fields in these domains, together with an analysis of the structure of the field. Classes of special functions used to construct uniform asymptotic expansions of wave fields are generally described together with the properties of these classes and the methods of computation.