Recursion operators.
Article Recursion operators for dispersionless integrable systems in...
rsolve({y(n) = n*y(n-1), y(0)=1}, y); But the PDEs can be hard to solve.
Yes, for instance the package Jets we used for computations in the article linked in the question:
http://jets.math.slu.cz
The package Jets as stated above can successfully handle such type of computations.
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