So the partial differential equation is:

$\frac{\partial h}{\partial t} =\frac{\partial}{\partial x} (\frac{1}{3}h^3 \frac{\partial h}{\partial x})$

and $h = t^\alpha f(\xi) $, where $\xi=\frac{x}{t^\beta}$

I want to determine a relationship between constant $\alpha$ and $\beta$.

So I plug the $h$ into the original equation which gives me a mess. Am I doing something wrong?

  • $\begingroup$ Well, plugging $h$ into the equation seems to be the most natural thing to do. You got a mess? Maybe you actually were supposed to make some sense out of it. Or maybe you did something wrong. What exactly? How are we to know? $\endgroup$ – Ivan Neretin May 9 at 12:46

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