Abstract
We give a dispersionless Toda-like extension to the dispersionless Harry Dym (dDym) hierarchy. The extended dDym (EdDym) hierarchy has a dressing formulation, and its underlying solution structure can be investigated through the twistor construction. We show that additional symmetries of the solution space generate Backlund transformations of the EdDym hierarchy. We present some examples of constructing new solutions of the (2+1)-dimensional dDym and EdDym equations via Backlund transformations.
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