Abstract
This paper is concerned with a double nonlinear dispersive equation: the Sharma-Tasso-Olver equation. We propose an improvedG′/G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained. When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solutions are derived from the trigonometric function solutions. The improvedG′/G-expansion method is straightforward, concise and effective and can be applied to other nonlinear evolution equations in mathematical physics.
Highlights
IntroductionWe consider the following double nonlinear dispersive, integrable equation: ut
In this paper, we consider the following double nonlinear dispersive, integrable equation: ut + α(u3)x3 2 α (u2)xx αuxxx = (1)where α is a real parameter and u(x, t) is the unknown function depending on the temporal variable t and the spatial variable x
It is easy to see that the hyperbolic function solution can be rewritten at A21 < A22 and A21 > A22 as follows: u (x, t) = φ (ξ) =
Summary
We consider the following double nonlinear dispersive, integrable equation: ut. Where α is a real parameter and u(x, t) is the unknown function depending on the temporal variable t and the spatial variable x This equation contains both linear dispersive term αuxxx and the double nonlinear terms α(u2)xx and α(u3)x. Using the improved tanh function method in [6], the Sharma-TassoOlver equation with its fission and fusion has some exact solutions. In [7], some exact solution of the Sharma-TassoOlver equation is given by implying a generalized tanh function method for approximating some solutions which have been known. Some entirely new exact solitary wave solutions and periodic wave solutions of the Sharma-Tasso-Olver equation are obtained.
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