Potential Symmetries and Associated Conservation Laws with Application to Wave Equations

It has been shown that one can generate a class of nontrivial conservation laws for second-order partial differential equations using some recent results dealing with the action of any Lie–Bäcklund symmetry generator of the equivalentfirst-order system on the respective conservation law. These conservedvectors are nonlocal as they are constructed from associatednonlocal symmetries of the partial differential equation. The method canbe successfully extended to association with ‘genuine’ nonlocal(potential) symmetries. However, it usually involves solving moredifficult systems of partial differential equations which may not alwaysbe easy to uncouple.