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On the Linearization of Second-Order Differential and Difference Equations

Vladimir Dorodnitsyn
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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.

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Vladimir Dorodnitsyn. 2006-08-16. On the Linearization of Second-Order Differential and Difference Equations. https://doi.org/10.3842/sigma.2006.065

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