Abstract

It is shown that the Harry Dym equation in 2+1 dimensions is linked by a reciprocal Bäcklund transformation to the singularity manifold equation generated by application of the Painlevé test to the Kadomtsev-Petviashvili equation. Invariance of the manifold equation under a Möbius transformation induces a novel involutory invariance of the original (2+1)-dimensional Dym equation.

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