Classical and partial symmetries of the Benney equation

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DOI:

https://doi.org/10.26637/mjm301/008

Abstract

Lie symmetry group method is applied to study Benney equation. The symmetry group and its optimal system are given,and group invariant solutions associated to the symmetries are obtained. Also the structure of the Lie algebra symmetries is determined. Mainly, we have compared one of the resolved analitical solutions of the Benney equation with one of it’s numerical solutions which is obtained via homotopy perturbation method in [4].

Keywords:

Lie group analysis, Partial symmetry, Symmetry group, Optimal system, Invariant solution, Benney equation

Mathematics Subject Classification:

53A55, 53B21
  • Mehdi Nadjafikhah Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 1684613114, I.R.IRAN.
  • Omid Chekini Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 1684613114, I.R.IRAN.
  • Pages: 86-92
  • Date Published: 01-01-2015
  • Vol. 3 No. 01 (2015): Malaya Journal of Matematik (MJM)

S. Lie, Theories der Tranformationgrippen, Dritter und Letzter Abschnitt, Teubner, Leipzig, 1893.

PJ. Olver, Eq̨uizdence, Inariont and Symumetry, Cambridge university press, Cambridge university press, Cambridge 1995.

P.]. Olver, Applications of Lie Groips to Differential Equations, Second edition, GTM, Vol. 107, Springer Verlage, New York, 1993

F. Wang, W, Li, H. Zhang, A new extended homotopy perturbation method for nonlinear differential equations, Mathematical and Computer Modellimg, 55(2012), 1471-1477. DOI: https://doi.org/10.1016/j.mcm.2011.10.029

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Published

01-01-2015

How to Cite

Mehdi Nadjafikhah, and Omid Chekini. “Classical and Partial Symmetries of the Benney Equation”. Malaya Journal of Matematik, vol. 3, no. 01, Jan. 2015, pp. 86-92, doi:10.26637/mjm301/008.

Issue

Vol. 3 No. 01 (2015): Malaya Journal of Matematik (MJM)

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Articles

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Copyright (c) 2015 MJM

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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