Group properties and invariant solutions of a sixth-order thin film equation in viscous fluid

TL;DR

This paper employs group theoretical methods to analyze a sixth-order thin film equation modeling viscous fluid flow, classifying symmetries and constructing invariant solutions with physical relevance.

Contribution

It provides the first comprehensive Lie group classification and invariant solutions for this generalized sixth-order thin film equation.

Findings

Identified the Lie symmetries and algebra of the equation.

Constructed physically significant invariant solutions.

Discovered solutions like sink, source, traveling-wave, waiting-time, and blow-up solutions.

Abstract

Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general Lie group classification of point symmetries, its Lie algebra, and the equivalence group are obtained. Similar reductions are performed and invariant solutions are constructed. It is found that some similarity solutions are of great physical interest such as sink and source solutions, travelling-wave solutions, waiting-time solutions, and blow-up solutions.