Wouldn't you have to be brain dead to think that this was a wave equation, when in fact it is just a gas momentum balance? No of course not. Who but a specialist in the field would spot the difference? Or that in the form you have cut and paste it, it is anything but a linear equation (non-linear hyperbolic function as it happens). How? The mathematics behind the links you posted are hard even for post-graduates in a mathematically focused degree discipline. Totally incomprehensible for anybody else. So just what are you trying to prove here? That you understand this stuff and we don't? Think again, sunshine.