Group Analysis and Heir-Equations for Thin Liquid Films

DOI

10.1142/S1402925109000078How to use a DOI?

Keywords

Group analysis; nonclassical symmetries

Abstract

Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and η-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.

Copyright

© 2009 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - S. Martini
AU  - N. Ciccoli
AU  - M. C. Nucci
PY  - 2021
DA  - 2021/01/07
TI  - Group Analysis and Heir-Equations for Thin Liquid Films
JO  - Journal of Nonlinear Mathematical Physics
SP  - 77
EP  - 92
VL  - 16
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000078
DO  - 10.1142/S1402925109000078
ID  - Martini2021
ER  -