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SIGMA 2 (2006), 065, 15 pages nlin.SI/0608038
https://doi.org/10.3842/SIGMA.2006.065
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
Received November 28, 2005, in final form July 13, 2006; Published online August 15, 2006
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.
Key words:
non-point transformations; second-order ordinary differential and difference equations; linearization; superposition principle.
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References
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Continuous symmetries of Lagrangians and exact solutions of
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