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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

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  • $\begingroup$ The title was changed by an unknown to me person after my edit. The result of my edit was "How to find the implicit solution of PDE's?". I added ? at the end. $\endgroup$
    – user64494
    Commented Aug 8, 2019 at 17:35
  • $\begingroup$ @user64494 I'm not the one who did it. I just re-edited my title as you said. $\endgroup$
    – J.A
    Commented Aug 8, 2019 at 19:11

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