Cecil Moore wrote:

I(x,t) = Imax sin(kx) cos(wt)

For any point location 'x', it can be seen that the standing
wave current is not "flowing" in the ordinary sense of the word
but rather, is just oscillating in place at that fixed point.

According to the equation you provide above, for any point location
'x', the phase of the current varies continuously with t. Presumably
that is what it means to just oscillate in place.

73, ac6xg