International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 531-540

Space-time caustics

Arthur D. Gorman

Department of Engineering Science, Lafayette College, Easton 18042, Pennsylvania, USA

Received 18 November 1985; Revised 8 April 1986

Copyright © 1986 Arthur D. Gorman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear differential equations modelling wave propagation in spatially inhomogeneous media at caustic (turning) points. Here the formalism is adapted to determine a class of asymptotic solutions at caustic points for those equations modelling wave propagation in media with both spatial and temporal inhomogeneities. The analogous Schrodinger equation is also considered.