Symmetry group analysis and similarity reductions of the thin film equation

Subject Areas : Geometry

M. Jafari ¹ , A. Tanhaeivash ²

1 - Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran

Received: 2021-10-07 Accepted : 2021-12-08 Published : 2021-12-14

Keywords: Thin film equation, Lie symmetry group, similarity reduction, optimal system,

Abstract :

In this article, by using the Lie symmetry method, we find the Lie symmetry group of the thin film equation. Also, the one-dimensional optimal system of Lie subalgebras is obtained. Then, we calculate the similarity reductions of the thin film equation and classify them by using the optimal system.

References:

[1] Y. Alipour Fakhri, Y. Azadi, The moving frame method and invariant subspace under parametric group actions, J. Linear. Topological. Algebra. 10 (2021), 217-224.

[2] Y. Aryanejad, Symmetry analysis of wave equation on conformally flat spaces, J. Geometry. Physics. 161 (1) (2021), 161:104029.

[3] G. W. Bluman, S. C. Anco, Symmetry and Integeration Methods for Differential Equations, Springer, New York, 2004.

[4] G. W. Bluman, A. F. Cheviakov, S. C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Appl. Math. Sciences, Vol. 168, Springer, New York, 2010.

[5] G. W. Bluman, J. D. Cole, Similarity Methods for Differential equations, Appl. Math. Sci., No. 13, Springer-Verlag, New York, 1974.

[6] G. W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer, New York, 1989.

[7] B. J. Cantwell, Introduction to Symmetry Analysis, Cambridge University Press, 2002.

[8] V. A. Galaktionov, S. R. Svirshchevskii, Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics, Chapman and Hall/CRC, London, 2007.

[9] W. Gang-Wei, L. Xi-Qiang, Z. Ying-Yuan, Lie Symmetry analysis and invariant solutions of the generalized fifth-order KdV equation with variable coefficients, J. Appl. Math. Inform. 13 (1-2) (2013), 229-239.

[10] N. H. Ibragimov, S. V. Meleshko, A solution to the problem of invariants for parabolic equations, Commun. Nonlinear. Sci. Numer. Simulat. 14 (2009), 2551-2558.

[11] S. Lie, On integration of a class of linear partial differential equations by means of definite integrals, Arch. Math. 6 (1881), 328-368.

[12] H. Liu, J. Li, L. Liu, Y. Wei, Group classifications, optimal systems and exact solutions to the generalized Thomas equations, J. Math. Anal. Appl. 383 (2011), 400-408.

[13] P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986.

[14] L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.