Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2006-08-16
SIGMA 2 (2006), 065, 15 pages
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Scientific paper
10.3842/SIGMA.2006.065
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.
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