The recently proposed nonholonomic deformation of the KdV equation is solved through the inverse scattering method by constructing an AKNS-type Lax pair. Exact N -soliton solutions are found for the basic field and the deforming function showing an unusual accelerated (decelerated) motion. A two-fold integrable hierarchy is revealed, one with the usual higher order dispersion and the other with novel higher nonholonomic deformations.
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