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

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 Poincare upper half-plane; (ii) N - concentric circles centered at the origin; and, (iii) a hypercircle in the Poincare disk.

Automated summary

The study investigates the scattering of a plane wave in the hyperbolic plane, formulating the problem using the Lippmann-Schwinger equation and solving it exactly for barriers modeled as various geometric shapes.