For a1 you can get rid of the term lambda*h^a if you put h=A*(-lambda*t+H)^s, where H=H(x,t) is the new unknown function, s=1/(1-a), A=s^(1/(a-1)). However, I do not see you how you then can get rid of the explicit dependence on t in the resulting equation for H.
#Artur Thanks for the answer but with the transform you suggest you get rid of lambda^h^a but at the expenses of a generation of new terms due to the binomial structure of the transform.
Excuse me, but what is the point of the transformation? In the a=1 case, the resulting equation is only superficially simpler than the original one, since it still contains h, which now has to be thought of in terms of tau instead of t.
#Herbert Eliminating the additional term, you have a prototype diffusion-convection equation. With further constraints, like momentum conservation, you can obtain analytic solutions in terms of self-similar variables. Please read the attached pdf file.
Well, Eq. (5) in the new pdf does not contain h anymore, while Eq. (5) in the old pdf did, which was the main cause for my previous comment. Which Eq. (5) is the correct one?
The last one. The former was a misprint. If you use the suggested transform you can check it.
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