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.
It means the fourth derivative with respect to the same variable. It is written like that just to avoid long indices. For example :
$$u_{x^4} = u_{xxxx}, \; u_{y^4} = u_{yyyy}, \; u_{z^4} = u_{zzzz}$$