Potential symmetry generators and associated conservation laws of perturbed nonlinear equations

摘要

Some recent results on approximate Lie group methods and previously developed concepts on potential symmetries are extended and applied to (mainly) nonlinear systems perturbed by a small parameter. The potential (or auxilliary) form of the perturbed system necessarily requires a knowledge of an `approximate' conservation law of the system. We then also use knowledge of `approximate' potential symmetries to calculate new approximate potential conservation laws.