Exact accelerating solitons in nonholonomic deformation of the KdV equation with a two-fold integrable hierarchy

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.