We prove that a second-order Monge-Ampere equation for one function of two variables is connected to the flat wave equations by a Backlund transformation if and only if it is integrable by the method of Darboux at second order. The proof relies on a geometric formulation of a Backlund transformation as a certain type of exterior differential system and its associated differential invariants. This is joint work with Thomas Ivey of the College of Charleston.

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