Approximate symmetries and conservation laws with applications

The relationship between the approximate Lie-Backlund symmetries and the ap proximate conserved forms of a perturbed equation is studied. It is shown t hat a hierarchy of identities exists by which the components of the approxi mate conserved vector or the associated approximate Lie-Backlund symmetries are determined by recursive formulas. The results are applied to certain c lasses of linear and nonlinear wave equations as well as a perturbed Kortew eg-de Vries equation. We construct approximate conservation laws for these equations without regard to a Lagrangian.