Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films

K. Charalambous, C. Sophocleous, P. G.L. Leach

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1 Citation (Scopus)

Abstract

In the modelling of the flow of thin films higher-order derivatives in the spatial variable are introduced to model nonlinear effects. We examine nonlinear evolution equations of the fifth and sixth orders in the spatial variable from the viewpoint of Lie symmetry analysis. Values of the parameters which allow for a greater number of Lie point symmetries are identified. As the equations can be recast in potential form, we consider their potential symmetries. We also consider the singularity properties of the corresponding steady-state equations.

Original languageEnglish
Pages (from-to)1949-1958
Number of pages10
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume18
Issue number8
DOIs
Publication statusPublished - Aug 2013

Keywords

  • Algebras and groups
  • Evolution partial differential equations
  • Lie symmetries
  • Singularity analysis
  • Thin films

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