First integrals of ordinary difference equations beyond Lagrangian methods
Exactly Solvable and Integrable Systems
2013-11-08 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1311.1597,
title = {First integrals of ordinary difference equations beyond Lagrangian methods},
author = {V. Dorodnitsyn and E. Kaptsov and R. Kozlov and P. Winternitz},
journal= {arXiv preprint arXiv:1311.1597},
year = {2013}
}