Symmetry group analysis and similarity reductions of the thin film equation

Journal of Linear and Topological Algebra

دوره 10، شماره 04، اسفند 2021، صفحه 287-293   

نوع مقاله: Research Paper

نویسندگان

M. Jafari^* ؛ A. Tanhaeivash

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

چکیده

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.

کلیدواژه‌ها

Thin film equation؛ Lie symmetry group؛ similarity reduction؛ optimal system

مراجع

[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.