ON WAVE FRONTS AND BOUNDARY WAVES,
Abstract
For a scalar field governed by a linear hyperbolic partial differential equation with constant coefficients, the wave fronts and their singularities arising from a point source in space-time are studied. The calculus of distributions is employed to represent the elementary solution, and a method of stationary phase to describe asymptotically its singularities. The occurrence of coincident characteristic roots, giving rise to ruled surface singularities, is first considered. The main portion of the paper concerns the reflection of the waves at a plane boundary, where several further types of waves can arise. Head waves and branch waves arise from branch points associated with real and complex normal roots. The Rayleigh and supersonic waves arise from poles of a certain boundary discriminant, and the latter type has an extended domain of dependence. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1963
- Accession Number
- AD0431098
Entities
People
- G. F. D. Duff
Organizations
- University of Wisconsin–Madison