Symmetry-enhancing for a thin film equation

Abstract

This thesis is concerned with the construction of new one-parameter symmetry groups and similarity solutions for a generalisation of the one-dimensional thin film equation by the method of symmetry-enhancing constraints involving judicious equation-splitting. Firstly by Lie classical analysis we obtain symmetry groups and similarity solutions of this thin film equation. Via the Bluman-Cole non-classical procedure, we then construct non-classical symmetry groups of this thin film equation and compare them to the classical symmetry groups we derive for this equation. Next we apply the method of symmetry-enhancing constraints to this thin film equation, obtaining new Lie symmetry groups for this equation. We construct similarity solutions for this thin film equation in association with these new groups. Subsequently we retrieve further new symmetry groups for this thin film equation by an approach combining the method of symmetry-enhancing constraints and the Bluman-Cole non-classical procedure. We derive similarity solutions for this thin film equation in connection with these new groups. Then we incorporate nontrivial functions into a partition (of this thin film equation) which has previously led to new Lie symmetry groups. The resulting system admits new Lie symmetry groups. We recover similarity solutions for this system and hence for the thin film equation in question. Finally we attempt to derive potential symmetries for this thin film equation but our investigations reveal that none occur for this equation.

Date of Award	2008
Original language	English