Connection for Wave Modulation.
Abstract
A new approach is described to the connection of wave amplitudes across the turning points and singular points of second-order, linear, analytic, ordinary differential equations which can describe the modulation of physical waves or oscillators. The general class of singular points thereby defined contains many irregular ones of greater complexity than have been accessible before; however, genuine coalescence of singular points is not here considered. The asymptotic connection formulae are shown to result directly from the branch structure of the singular point; indeed, to a first approximation, they reflect merely the gross, local branch structure. The proof relates the local structure of the solutions at the singular point to the asymptotic wave structure by a limit process justified by symmetry bounds.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1981
- Accession Number
- ADA110474
Entities
People
- J. F. Painter
- R. E. Meyer
Organizations
- University of Wisconsin–Madison