# Meaning of numerals in partial differential equation notation

Could someone please explain this notation for a partial differential equation?

The example is from encyclopedia of mathematics.

I'm familiar with the notation $u_x=\frac{\delta{u}}{\delta{x}}$.

But I do not understand what the numeral 4 represents in $u_{x^4}$.

Is it the fourth derivate perhaps?

This type of notation is not explained on the wikipedia page for PDE notation.

• My guess would be that this is formatted as (for example) u_{x^4}, which is rendered here as $u_{x^4}$. This would be a slightly nonstandard way of writing $u_{xxxx}$, i.e. the fourth derivative in the direction of $x$. Personally, I would prefer $$\frac{\partial^4}{\partial x^4} u,$$ or possibly, using multiindex notation, $\partial^{(4,0,0)} u(x,y,z)$. – Xander Henderson May 22 at 0:35

$$u_{x^4} = u_{xxxx}, \; u_{y^4} = u_{yyyy}, \; u_{z^4} = u_{zzzz}$$