Preliminary group classification of a class of fourth-order evolution equations

Abstract

We perform preliminary group classification of a class of fourth-order evolution equations in one spatial variable. Following the approach developed by Basarab-Horwath et al. [Acta Appl. Math. 69, 43 (2001)], we construct all inequivalent partial differential equations belonging to the class in question which admit semisimple Lie groups. In addition, we describe all fourth-order evolution equations from the class under consideration which are invariant under solvable Lie groups of dimension n<=4. We have constructed all Galilei-invariant equations belonging to the class of evolution differential equations under study. The list of so obtained invariant equations contains both the well-known fourth-order evolution equations and a variety of new ones possessing rich symmetry and as such may be used to model nonlinear processes in physics, chemistry, and biology.