Background
Let's say I have a field/fluid which occupies a volume element $dV$ then equation of motion is given by:
$$ \left( \frac{1}{c} \frac{\partial V}{\partial t} \right)^2 = \phi_{xy}^2 + \phi_{yz}^2 + \phi_{zx}^2 $$
where $t$ is time, $c$ is a constant, $\phi_{xy}$ is the flux through the $xy$ plane of of the surface, $\phi_{yz}$ is the flux through the $yz$ plane of the surface and $\phi_{zx}$ is the flux through the surface of the $zx$ plane.
Question
What are the invariants of this field? For example is it radially symmetric? Is there some nice way to visualize it's time evolution?