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

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

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DOI: 10.4236/am.2012.31002                

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.

Keywords

Characteristic Function Method; Wu-Zhang Equation

Conflicts of Interest

The authors declare no conflicts of interest.

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