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First integrals of difference equations which do not possess a variational formulation |
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| Authors: | P Winternitz V A Dorodnitsyn E I Kaptsov R V Kozlov |
| Institution: | 1. Centre de Recherches Mathématiques et Département de mathématiques et de statistique, Université de Montréal, Montréal, QC, H3C 3J7, Canada 2. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia 3. NPO Verteks, Turgenieva ul. 131/1, Krasnodar, 350051, Russia 4. Department of Business and Management Science, Norwegian School of Economics, Helleveien 30, Bergen, 5045, Norway |
| Abstract: | The paper presents a new method for finding first integrals of difference equations which do not possess Lagrangians, nor Hamiltonians. In this paper we consider ordinary differential and difference equations. As an example we solve a third order nonlinear ordinary differential equation and its invariant discretization using three first integrals obtained by means of this method. |
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