Roman Kozlov, Norwegian School of Economics and CRM

The adjoint equation method for constructing first integrals of difference equations

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. If a sufficient amount of independent first integrals is known, it possible to find the general solution of the discrete equations. The method can also be applied to difference schemes which provide discretizations of ODEs.