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.