Application of the three-dimensional telegraph equation to cosmic-ray transport
arXiv:1606.08272 · doi:10.1088/1674-4527/16/10/162
Abstract
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the Klein-Gordon equation, the telegraph equation can be solved in closed form. Illustrative examples are used to discuss the qualitative differences to the diffusion solution. The comparison with a numerical test-particle simulation reveals that some features of an intensity profile can be better explained using the telegraph approach.
13 pages, 6 figures, accepted for publication in "Research in Astronomy and Astrophysics"