ANALYSIS OF A FOURTH-ORDER NONLINEAR EVOLUTION EQUATION BY CLASSICAL AND NON-CLASSICAL SYMMETRY METHODS

In this paper the classical Lie group formalism is applied to deduce new classes of solutions of a nonlinear partial differential equation (nPDE) of the fourth order, the so called Derrida-Lebowitz-Speer-Spohn equation (DLSS) importantly in several physical applications. Up to now no carefully performed symmetry analysis is available. Therefore we determine the classical Lie point symmetries including algebraic properties. Similarity solutions are given as well as new nonlinear transformations could derived. It is further shown that algebraic solution techniques fail so a symmetry analysis justifies the application. In addition, we discuss approximate symmetries to the first time and moreover we shall see that the DLSS equation admits a new symmetry, the so called potential symmetry. Broadly speaking, the analysis allows one to deduce wider classes of new unknown solutions either of practical and theoretical usage