Irregular Points of Modulation.
Abstract
The local theory of singular points is extended to a large class of linear, second-order, ordinary differential equations which can be physical Schroedinger equations or govern the modulation of real oscillators or waves. In addition to Langer's fractional turning points, such equations admit highly irregular points at which the coefficients of the differential equation can be almost arbitrarily multivalued. Genuine coalescence of singular points, however, is not considered. A local representation of solution structure is established which generalizes Frobenius' method of power series. Some results on solution symmetry have striking, global implications in the shortwave limit. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1981
- Accession Number
- ADA110473
Entities
People
- J. F. Painter
- R. E. Meyer
Organizations
- University of Wisconsin–Madison