ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 10 (2021), no.5, 2611–2624 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.10.5.24 NONLINEAR DIFFUSION EQUATION WITH A PERTURBED CONVECTIONTERM: POTENTIAL SYMMETRIES WITH RESPECT TO THE SECOND CONSERVATION LAW Ojen Kumar Narain 1 and Fazal Mahmood Mahomed ABSTRACT. We consider the nonlinear diffusion equation with a perturbed con- vection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed equation with respect to the other conservation law. 1. I NTRODUCTION Certain nonlinear PDEs that arise in applications depend on a small param- eter. Thus it is of importance to find approximate solutions. Baikov et al ( [1], [2], [3]) developed the theory and applications of the approximate sym- metry group method to find approximate invariant solutions of DEs amongst other things. 1 corresponding author 2020 Mathematics Subject Classification. 35L65, 70G65, 70S105. Key words and phrases. Nonlinear diffusion equation, potential symmetries, conservation law, approximate potential symmetries. Submitted: 09.05.2021; Accepted: 22.05.2021; Published: 26.05.2021. 2611