Exact solutions of nonlinear wave equations using \((G^\prime/G, 1/G)\)-expansion method. (English) Zbl 1319.34008
Summary: The \((G^\prime/G, 1/G)\)-expansion method with the aid of Maple is used to obtain new exact travelling wave solutions of the Hamiltonian amplitude equation and the Broer-Kaup equations arise in the analysis of various problems in fluid mechanics, theoretical physics. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. The method demonstrates power, reliability and efficiency. The method also presents a wider applicability for handling nonlinear wave equations.
MSC:
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 35C07 | Traveling wave solutions |
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 35L05 | Wave equation |
Keywords:
exact solutions; \((G^\prime/G, 1/G)\)-expansion method; the Hamiltonian amplitude equation; the Broer-Kaup equationsSoftware:
MapleReferences:
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