Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations

We propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the Ablowitz-Kaup-Newell-Segur (AKNS) and the Kaup-Newell classes based on the simple idea of dimensional analysis and detecting the building blocks of the Lax pair. Along with the well-known equations, we discover a novel integrable hierarchy of higher order nonholonomic deformations for the AKNS family, e.g., the Korteweg-de Vries (KdV), the modified KdV, the nonlinear Schroumldinger, and the sine-Gordon equation, showing thus a twofold universality of the recently found deformation for the KdV equation [A. Karsu , J. Math. Phys. 49, 073516 (2008)].