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arXiv · 1311.1597

First integrals of ordinary difference equations beyond Lagrangian methods

V. Dorodnitsyn·E. Kaptsov·R. Kozlov·P. Winternitz
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Abstract

A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The method is based on a newly established identity which links symmetries of the underlying discrete equations, solutions of the discrete adjoint equations and first integrals. The method is applied to invariant mappings and discretizations of a second order and a third order ODEs. In examples the set of independent first integrals makes it possible to find the general solution of the discrete equations. The method is compared to a direct method of constructing first integrals.

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V. Dorodnitsyn, E. Kaptsov, R. Kozlov, P. Winternitz. 2013-11-07. First integrals of ordinary difference equations beyond Lagrangian methods. https://arxiv.org/abs/1311.1597

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