Scalar Klein--Gordon equation and its analytically continued dispersion diagram
Mathematical Physics
2020-02-03 v1 math.MP
Abstract
The scalar Klein-Gordon equation describes wave motion in a waveguide with a cut-off. For example, the displacement of an elastic cord anchored to a solid base by elastic elements can be described by the scalar Klein-Gordon equation. We analyse this equation using the concept of analytical continuation of dispersion diagram. Particularly, it is shown that the dispersion diagram is topologically equivalent to a tube analytically embedded in two-dimensional complex space. The corresponding Fourier integral is studied on this tube using the Cauchy's theorem. The basic properties of the scalar Klein-Gordon equation are established.
Cite
@article{arxiv.2001.11765,
title = {Scalar Klein--Gordon equation and its analytically continued dispersion diagram},
author = {A. I. Korolkov and A. V. Shanin},
journal= {arXiv preprint arXiv:2001.11765},
year = {2020}
}