So I'm fairly confused at the moment.
For reference, I'm reading this document, and the current area of interest is Section 7: Characteristic Surfaces for Planar Waves.
I'm not gonna give too much context because I'm pretty sure this is just a math problem. I could be wrong
I'm attaching a [;\LaTeX;] document of my own because writing it up in here is a pain.
Here is the my attached writeup (Please let me know if you cannot view this document) (This is also now a complete description of what I did)
Thanks, and let me know if you have any additional questions, I almost certainly left something important out.