Nonholonomic deformation of KdV and mKdV equations and their symmetries, hierarchies and integrability

The recent concept of integrable nonholonomic deformation found for the Korteweg–de Vries (KdV) equation is extended to the modified KdV (mKdV) equation and generalized to the AKNS system. For the deformed mKdV equation we find a matrix Lax pair, a novel two-fold integrable hierarchy and exact N -soliton solutions exhibiting unusual accelerating motion. We show that both the deformed KdV and mKdV systems possess infinitely many generalized symmetries, conserved quantities and a recursion operator.