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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##.

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# Undoing Similarity Transforms

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