Abstract
In this paper, the \((G'/G)\)-expansion method is employed to construct more general solitary wave solutions of three special types of Boussinesq equation, namely Boussinesq equation, improved Boussinesq equation and variant Boussinesq equation, where the French scientist Joseph Valentin Boussinesq (1842–1929) described in the 1870s model equations for the propagation of long waves on the surface of water with a small amplitude. Our work is motivated by the fact that the \((G'/G)\)-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.
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