Features of the Use of Symbolic Calculations for Constructing Wave Field Local Asymptotics Using Catastrophe Theory

Abstract

Base on symbol calculation a local asymptotic method is developed that describes the diffraction focusing of electromagnetic fields in the case when a family of primary (geometrooptical) and secondary (edge) rays form focusings of the cuspoid type A2 (wave catastrophe F4). Mathematical modeling of the unfolding coefficients and the traveling wave phase was performed. Explicit expressions for the parameters of unfolding are obtained.