I wanted to know if there were hints and educated guesses to find the implicit solutions of complicated PDE's.

I'm currently dealing with functions of the form $f(r,t)$.

I know that a lot of time a solution can be found in the form : $t=ar+A(f)$.

But when it doesn't work, instead of starting looking for all types of solutions, are there things that we can find in the nature of the equation ?

One of the equation I'm dealing with is $\partial_t f = \partial_x((f^2-1)\partial_{x}f)-\partial_{xxxx}f $.

I know that Maple can find a lot of time the solution but I don't have it.

So if you have some general advices or references they are welcome