Scattering in the Poincaré disk and in the Poincaré upper half-plane

Abstract

We investigate the scattering of a plane wave in the hyperbolic plane. We formulate the problem in terms of the Lippmann-Schwinger equation and solve it exactly for barriers modeled as Dirac delta functions running along: (i) N − horizontal lines in the Poincaré upper half-plane; (ii) N − concentric circles centered at the origin; and, (iii) a hypercircle in the Poincaré disk.