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

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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.

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The authors declare no conflicts of interest.

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M. Helal, M. Mekky and E. Mohamed, "The Characteristic Function Method and Its Application to (1 + 1)-Dimensional Dispersive Long Wave Equation,"

*Applied Mathematics*, Vol. 3 No. 1, 2012, pp. 12-18. doi: 10.4236/am.2012.31002.

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