Potential symmetry generators of some perturbed nonlinear evolution related equations

Abstract

Some recent results on approximate Lie group methods and previously developed concepts on potential symmetries are extended and applied to nonlinear systems perturbed to some order by a small parameter. The potential (or auxiliary) form of the perturbed system necessarily requires knowledge of an "approximate" conservation law of the system. We make an analysis on a perturbed Burgers equation and discuss other nonlinear equations where the results are applicable.