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P. J. Olever, “Applications of Lie Groups to Differential Equations,” Springer, New York, 1968.

has been cited by the following article:

• TITLE: The Characteristic Function Method and Its Application to (1 + 1)-Dimensional Dispersive Long Wave Equation

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

  KEYWORDS: Characteristic Function Method; Wu-Zhang Equation

  JOURNAL NAME: Applied Mathematics, Vol.3 No.1, January 4, 2012

  ABSTRACT: In this paper, the characteristic function method is applied to seek traveling wave solutions of nonlinear partial differential equations in a unified way. We consider the Wu-Zhang equation (which describes (1 + 1)-dimensional disper-sive long wave). The equations governing the wave propagation consist of a pair of non linear partial differential equations. The characteristic function method reduces the system of nonlinear partial differential equations to a system of nonlinear ordinary differential equations which is solved via the shooting method, coupled with Rungekutta scheme. The results include kink-profile solitary wave solutions, periodic wave solutions and rational solutions. As an illustrative example, the properties of some soliton solutions for Wu-Zhang equation are shown by some figures.