1307.7585 (P. Winternitz et al.)

First integrals of ordinary difference equations which do not possess a
variational formulation    [PDF]

P. Winternitz, V. Dorodnitsyn, E. Kaptsov, R. Kozlov

The paper presents a new method for finding first integrals of ordinary difference equations which do not possess Lagrangians, nor Hamiltonians. As an example we solve a third order nonlinear ordinary differential equation and its invariant discretization using three first integrals obtained using this method.

View original: http://arxiv.org/abs/1307.7585