A general theorem on conservation laws for arbitrary difference equations isproved. The theorem is based on an introduction of an adjoint system relatedwith a given difference system, and it does not require the existence of adifference Lagrangian. It is proved that the system, combined by the originalsystem and its adjoint system, is governed by a variational principle, whichinherits all symmetries of the original system. Noether's theorem can then beapplied. With some special techniques, e.g. self-adjointness properties, thisallows us to obtain conservation laws for difference equations, which are notnecessary governed by Lagrangian formalisms.
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