Ok, so I've been trying to solve this for a while now and I don't seem to get anywhere. Hope someone can point in the right direction.
We have the PDE
where
are independent variables and
.
So, I know that the equations for the characteristics in this case are
but, I don't see how I can obtain
from here, I've tried playing with the coefficients in the original, isolating
or
but that gets me nowhere. I'm thinking of proposing the curve
as a characteristic, but I haven't checked if it is. So, if someone could give any hints as to how to solve this it would be appreciated.