This article is cited in 5 papers

On the Linearization of Second-Order Differential and Difference Equations

Vladimir Dorodnitsyn

Keldysh Institute of Applied Mathematics of Russian Academy of Science, 4 Miusskaya Sq., Moscow, 125047 Russia

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.

Keywords: non-point transformations; second-order ordinary differential and difference equations; linearization; superposition principle.

MSC: 34C14; 34C20; 39A05; 65L12; 70H33

Received: November 28, 2005; in final form July 13, 2006; Published online August 16, 2006

Language: English

DOI: 10.3842/SIGMA.2006.065

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ArXiv: nlin.SI/0608038