Abstract
An N-cusp soliton solution of the Harry Dym equation (HDE) is constructed explicitly. The proposed approach is based on the algebraic 'effectivization' of the reciprocal links between the systems consisting of N higher-order analogues of the HDE and the corresponding analogues of the KdV equation. An important role in the discussed scheme belongs to the reciprocal auto-Backlund transformation for the Dym hierarchy.
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