# Undoing Similarity Transforms

1. Jun 30, 2015

### joshmccraney

Hi PF!

I am wondering how to bring boundary conditions through a similarity transform. The transform is as follows $$h(z,\tau) = \tau^a F(\eta)\\ \eta = C_2 z \tau^b\\L=\eta_{tip} C_2^{-1}\tau^{-b}$$ Before I continue, I have a pdf of a tex doc I made for this, but since I don't have the same syntax as these forums it would be easier if I could pm someone with the problem.

If not, please let me know, as I am totally fine with posting all of the work. I just want someone to check and see if my work is okay.

Thanks so much!

Actually, for ease I'll post my work for one here now so you get a better idea of what I'm talking about. The first boundary condition is $F^+(\eta^+)=0$ where $\eta^+=1$ so essentially $F^+(1)=0$. I should say $F^+\lambda^2=F$ and $\eta^+ \lambda = \eta$. Now we have $F^+(1)=0 \implies \lambda^{-2} F(1)=0 \implies F(1)=0$.

From here $\eta=1\implies z=C_2^{-1} \tau^{-b}$ and thus $h(C_2^{-1} \tau^{-b},\tau) = \tau^a F(1) = 0$.

Last edited: Jun 30, 2015
2. Jul 5, 2015