
Symmetry in Nonlinear Mathematical Physics  2009
Liliia Myroniuk (Lesya Ukrainka Volyn National University, Lutsk, Ukraine)
Lie symmetries and exact solutions of the generalized thin film equation
Abstract:
A symmetry group classification for fourthorder
reactiondiffusion equations, allowing for both secondorder and
fourthorder diffusion terms, is carried out. The fourth order
equations are treated, firstly, as systems of secondorder
equations that bears some resemblance to systems of coupled
reactiondiffusion equations with cross diffusion, secondly, as
systems of a of secondorder equation and two firstorder equations.
The paper generalizes the results of Lie symmetry analysis derived
earlier for particular cases of these equations. A wide range of
exact solutions are constructed using Lie symmetry reductions of the
reactiondiffusion systems
to the ordinary differential equations.
The solutions include some unusual structures as well as the familiar types that regularly occur
in symmetry reductions, namely selfsimilar solutions, decelerating and decaying traveling waves,
and steady states.

