Local Asymptotics of Unfoldings of Edge and Corner Catastrophes

Abstract

Using symbolic calculations, a method of local asymptotics is developed, which describes the diffraction focusing of electromagnetic and acoustic fields for edge and corner catastrophes. Explicit expressions are found for the unfolding coefficients, the functional module, and the phase of the traveling wave, when the family of primary (geometrical-optical) and secondary (edge) rays form focuses on the cuspoid $${\mathrm{\boldsymbol A}}_{\mathrm{2}}$$ type (simple edge catastrophe $${\mathrm{\boldsymbol F}}_{\mathrm{4}}$$ ), when the family of primary and secondary rays form focuses on the $${\mathrm{\boldsymbol A}}_{\mathrm{3}}$$ type (unimodal edge catastrophe $${\mathrm{\boldsymbol K}}_{\mathrm{4,2}}$$ ), as well as for a corner catastrophe $${\mathrm{\boldsymbol A}_{1}}^{4}$$ .