I'm working on modelling a drip running down a wall, which is modelled at $t=0$
by
$h=1+e^{-x^2}$
And as $t$ increases, I've found it to be modelled by
$h=1+e^{-(x-h^2t)^2}$
Obviously, subbing $h$ into itself doesn't help whatsoever
I want to sketch how the drop would look like, and how far down the wall it would be at $t=0,1,2,3$ to illustrate what's happening. I'm also asked why this model might break down...
The obvious thing I can see is that its shifted $h^2t$ to the right, but of course, $h$ depends on $x,t$ which confuses me.
Any help with how this transformation makes the drip behave would be massively appreciated
