On the Linearization of Second-Order Differential and Difference Equations
Abstract
This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and Noether-type integration technique. It turned out that there exist nonlinear superposition principles for solutions of special second-order ordinary difference equations which possess Lie group symmetries. This superposition springs from the linearization of second-order ordinary difference equations by means of non-point transformations which act simultaneously on equations and meshes. These transformations become some sort of contact transformations in the continuous limit.
Cite
@article{arxiv.nlin/0608038,
title = {On the Linearization of Second-Order Differential and Difference Equations},
author = {Vladimir Dorodnitsyn},
journal= {arXiv preprint arXiv:nlin/0608038},
year = {2008}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/