Generalized extended tanh-function method and its application to \((1+1)\)-dimensional dispersive long wave equation. (English) Zbl 1019.35059
Summary: Making use of a new generalized ansatze, we present the generalized extended tanh-function method for constructing the exact solutions of nonlinear partial differential equations (NPDEs) in a unified way. Applying the generalized method, with the aid of Maple, we consider the Wu-Zhang equation (which describes \((1+1)\)-dimensional dispersive long wave). As a result, we can successfully obtain the solitary wave solutions that can be found by the extended tanh-function method and the modified extended tanh-function method. More importantly, for the equation, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary wave solutions, bell-profile solitary wave solutions, periodic wave solutions, rational solutions, singular solutions and other new formal solutions. As an illustrative sample, the properties of some soliton solutions for the Wu-Zhang equation are shown by some figures.
MSC:
| 35L05 | Wave equation |
| 35C05 | Solutions to PDEs in closed form |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 74J35 | Solitary waves in solid mechanics |
Software:
MapleReferences:
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