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

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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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