  Recently proposed nonholonomic deformation of the KdV equation is solved
through inverse scattering method by constructing AKNS-type Lax pair. Exact and
explicit 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 usual higher order dispersion and
the other with novel higher nonholonomic deformations.
