Potential symmetry generators and associated conservation laws of perturbed nonlinear equations A.H. Davison, A.H. Kara * School of Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South Africa Abstract Some recent results on approximate Lie group methods and previously developed concepts on potential symmetries are extended and applied to (mainly) nonlinear sys- tems 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. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Approximate potential generators; Conservation laws 1. Introduction The notions of nonlocal and potential symmetries associated with a partial differential equation (pde) have been widely investigated in the literature––the most popular being that by Bluman and Kumei [4]. As an example, we consider the nonlinear Burgers equation Rfx; t; ug (which arises in the modelling of turbulence) given by u xx  uu x  u t ¼ 0: ð1:1Þ * Corresponding author. E-mail address: kara@maths.wits.ac.za (A.H. Kara). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2003.07.012 Applied Mathematics and Computation 156 (2004) 271–285 www.elsevier.com/locate/amc