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Recently proposed nonholonomic deformation of the KdV equation is solvedthrough inverse scattering method by constructing AKNS-type Lax pair. Exact andexplicit N-soliton solutions are found for the basic field and the deformingfunction showing an unusual accelerated (decelerated) motion. A two-foldintegrable hierarchy is revealed, one with usual higher order dispersion andthe other with novel higher nonholonomic deformations.

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