53rd Midwest PDE Seminar March 19-21, 2004 Department of Mathematics University of Missouri

Giorgio Talenti University of Florence, Italy
Analysis of a Bäcklund transformation

Abstract

Let x and y denote rectangular coordinates in the Euclidean plane, and let n be a real-valued, strictly positive, sufficiently smooth function of x and y. We offer a theory of the following equation

all of whose solutions are complex-valued. This equation relates both to geo-metrical optics and to alternative asymptotic expansions of a monochromatic electromagnetic field that propagates past a caustic.