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M. S. Velan and M. Lakshmanan, “Lie Symmetries and Invariant Solutions of the Shallow-Water Equation,” International Journal of Non-Linear Mechanics, Vol. 31, No. 3, 1996, pp. 339-344. doi:10.1016/0020-7462(95)00063-1

has been cited by the following article:

• TITLE: A Similarity Technique for Solving Two-Layer Shallow-Water Equations

  AUTHORS: Magda M. Kassem, Medhat M. Helal, Mohammad L. Mekky, Emad A. Mohamed

  KEYWORDS: The Characteristic Function Method; The Two-Layer Shallow-Water Equations; Gravity Currents

  JOURNAL NAME: Applied Mathematics, Vol.3 No.4, April 27, 2012

  ABSTRACT: This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The application of the characteristic function method makes it possible to obtain the similarity forms depending on a group of infinitesimal transformations. Thus, the number of independent variables is reduced by one and the governing partial differential equations with the auxiliary conditions reduce to a system of ordinary differential equations with the appropriate auxiliary conditions. Numeric solutions are presented and discussed.