As explored in , the structure of the hyperbolic numbers encodes characteristics of two-dimensional Minkowski spacetime. Dierentiable functions on the hyperbolic numbers provide solutions to the wave equation. In this paper we analogize the method of conformal mappings to the hyperbolic numbers in order to provide solutions to the wave equation on given regions with given boundary constraints. As template solutions we use low-degree polynomials and the logarithm function, and as transformations we use polynomials and simple rational functions. We conjecture (and nearly show) that in general, the family of rational functions we use take hyperbolas to hyperbolas.
Estep, Samuel and Smith, Jonathan
Liberty University Digital Commons. Web. [xx Month xxxx].
Estep, Samuel and Smith, Jonathan (2019) "Making Waves" The Kabod 6( 1 (2019)), Article 4. Retrieved from https://digitalcommons.liberty.edu/kabod/vol6/iss1/4
Estep, Samuel and Smith, Jonathan "Making Waves" The Kabod 6 , no. 1 2019 (2019) Accessed [Month x, xxxx]. Liberty University Digital Commons.