I am trying to understand how can one apply the Hodograph transformation to a non-linear PDE. I read that this transformation implies the representation of the solution in the implicit form . So, if I have a function $f(x,t)$ which is defined by a certain non-linear PDE, by applying the above mentioned transformation, my equation will become an equation for the function $x(f,t)$ and the solution of this equation will represent the implicit solution of my original equation. I don't really understand the concept of implicit solution and why would I want such a solution , when I'm interested in finding $f(x,t)$ and not $x(f,t)$. Can one get from the solution for $x(f,t)$ to the solution for $f(x,t)$?
I have the feeling this is a very silly question, but if someone could help me with this problem I would really appreciate it.