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

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

2007-11-06

arxiv.org/abs/0711.0878v6

J. Math Phys. 50, 102702 (2009)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, 5 figures, Latex, Final version to be published in J. Math. Phys

Scientific paper

We propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the AKNS and the KN 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. for the KdV, the mKdV, the NLS and the SG equation, showing thus a two-fold universality of the recently found deformation for the KdV equation.

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