First integrals of ordinary difference equations beyond Lagrangian methods

2013/11/07 by В. А. Дородницын, Е. И. Капцов, Dorodnitsyn, V. +5
Mathematics · Physics and Astronomy · #39A99 #58J70 #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1311.1597

openalex publication_date 2013/11/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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