Applied Partial Differential Equations

Abstract

We aim to obtain complete group classification of Lie point symmetries and equivalence groups for various classes of differential equations and systems, such as, for example, generalized non-linear Schrödinger equations, equations describing heat transfer, the Liouville-Bratu-Gelfand Problem. We will establish the corresponding conservation laws. Since the studied evolutionary models do not have a variational structure, and therefore the classic Noether's Theorem does not apply, to obtain the conservation laws we will use Nail H. Ibragimov's Conservation Theorem, which allows us to establish conservation laws for any differential equations or systems. (AU)