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 Schrödinger, and the sine-Gordon equation, showing thus a twofold universality of the recently found deformation for the KdV equation [A. Karsu et al., J. Math. Phys. 49, 073516 (2008)].