Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations
Exactly Solvable and Integrable Systems
2015-05-13 v6 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.0711.0878,
title = {Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations},
author = {Anjan Kundu},
journal= {arXiv preprint arXiv:0711.0878},
year = {2015}
}
Comments
17 pages, 5 figures, Latex, Final version to be published in J. Math. Phys