Conservation law and Lie symmetry analysis of Foam Drainage equation

Abstract

In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation.

Keywords

• ‎lie group analysis
• ‎conservation law
• ‎ ‎optimal system
• ‎foam drainage equation
• nonclassical symmetry