  Given a function f(x, t), its fourth (symmetric) differential is a quartic
form in dx, dt. It is well-known that any quartic form in two variables can be
represented as a sum of three 4th powers of linear forms. The particular case
of two 4th powers is characterized by the vanishing of a catalecticant
determinant, which is a fourth order PDE for the function f. We demonstrate
that this PDE decouples in a direct sum of two Monge-Ampere equations. A higher
order generalization of this decomposition is also proposed.
